Analytical Chemistry - GRE Subject Test: Chemistry
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Michael's scale measures the mass of objects as consistently 
less than their actual mass. How would you describe the scale?
Michael's scale measures the mass of objects as consistently
Precision measures is how consistently a device records the same answer. In this case, Michael's scale is ALWAYS 
short. Even though it displays the wrong value, it is consistent. That means it is precise. Measuring a 
object will always display a mass of 
; the results are easily reproduced.
Accuracy is how well a device measures something against its accepted value. In this case, Michael's scale is not accurate because it is always off by 
.
Precision measures is how consistently a device records the same answer. In this case, Michael's scale is ALWAYS
Accuracy is how well a device measures something against its accepted value. In this case, Michael's scale is not accurate because it is always off by
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Michael buys several bags of balloons. On the package, it says that each bag has 100 balloons. He opens the bags and only one of them has 100 balloons inside; the other bags either have too many or too few.
How would you describe the bag of balloons with 100 balloons inside?
Michael buys several bags of balloons. On the package, it says that each bag has 100 balloons. He opens the bags and only one of them has 100 balloons inside; the other bags either have too many or too few.
How would you describe the bag of balloons with 100 balloons inside?
This bag is accurate because it provided the correct number of balloons, however, the process is not precise as the results were clearly not repeatable.
Accuracy deals with how close the measurement got to the accepted measurement. Precision deals with how consistent the measurement is. The bag with 100 balloons inside matched the claim made on the bag, meaning it was accurate. It was not precise because the other measurements show that the number of balloons is variable.
This bag is accurate because it provided the correct number of balloons, however, the process is not precise as the results were clearly not repeatable.
Accuracy deals with how close the measurement got to the accepted measurement. Precision deals with how consistent the measurement is. The bag with 100 balloons inside matched the claim made on the bag, meaning it was accurate. It was not precise because the other measurements show that the number of balloons is variable.
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An brand of fruit snacks claims that each bag of fruit snacks has a mass of 
. After weighing three bags, Wally observes the masses to be 
, 
, and 
.
How can Wally describe the accuracy and precision of the first bag he measured?
An brand of fruit snacks claims that each bag of fruit snacks has a mass of
How can Wally describe the accuracy and precision of the first bag he measured?
The claim for the mass of the first bag is accurate; the brand says there should be 
in each bag and there was 
in the first bag.
The claim on the first bag is not precise, as the results are not replicated universally throughout the experiment. The masses of the bags fluctuate, with the average of all three bags equal to 
.
The claim for the mass of the first bag is accurate; the brand says there should be
The claim on the first bag is not precise, as the results are not replicated universally throughout the experiment. The masses of the bags fluctuate, with the average of all three bags equal to
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A bowman is shooting arrows at a target. Which of the following demonstrates high accuracy but low precision?
A bowman is shooting arrows at a target. Which of the following demonstrates high accuracy but low precision?
Accuracy is measured as the degree of closeness to the actual measurement. In our case, accurate shots will hit the bullseye. Precision is measured as the degree of closeness of one measurement to the next. In our case, precise shots will be clustered together.
To get high accuracy but low precision, measurements must center around the target value but be variable. The bowman's arrows will not be clustered (low precision), but will be accurately distributed around the bullseye. If all the shots were averaged, the bullseye would be at the center.
Accuracy is measured as the degree of closeness to the actual measurement. In our case, accurate shots will hit the bullseye. Precision is measured as the degree of closeness of one measurement to the next. In our case, precise shots will be clustered together.
To get high accuracy but low precision, measurements must center around the target value but be variable. The bowman's arrows will not be clustered (low precision), but will be accurately distributed around the bullseye. If all the shots were averaged, the bullseye would be at the center.
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Which of these is an example of high accuracy?
Which of these is an example of high accuracy?
Accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
In contrast, precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
Accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
In contrast, precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
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Which of these is an example of high precision?
Which of these is an example of high precision?
Precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
In contrast, accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
Precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
In contrast, accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
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What is the molar concentration of a 2% by mass 
solution with a density of 
?
What is the molar concentration of a 2% by mass
By definition, 2% by mass means 2 grams of in every 100 grams of solution. In order to solve this problem, we may assume we are dealing with 100 grams of solution. We can use the density as a conversion factor to determine the volume of solution we are dealing with:
In order to calculate the number of moles of , we need to convert 2 grams of to moles using it's molecular weight. This is because we are assuming we are dealing 100 grams of a 2% solution.
In order to calculate molarity, we need to plug the moles and volumes calculated into the following equation:
By definition, 2% by mass means 2 grams of
In order to calculate the number of moles of
In order to calculate molarity, we need to plug the moles and volumes calculated into the following equation:
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Using the calibration curve given, if given the absorbance of 1.51, what would be the concentration?
Using the calibration curve given, if given the absorbance of 1.51, what would be the concentration?
A calibration curve is a graph that gives the relationship between a measured quantity and an analytical signal. In this question the analytical signal is absorbance and the measured quantity is the concentration. To answer this problem, simply determine where the absorbance value 1.5 is on the y-axis and find what point the x-axis crosses this absorbance.
A calibration curve is a graph that gives the relationship between a measured quantity and an analytical signal. In this question the analytical signal is absorbance and the measured quantity is the concentration. To answer this problem, simply determine where the absorbance value 1.5 is on the y-axis and find what point the x-axis crosses this absorbance.
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A researcher performs a Bradford assay to determine the quantity of an unknown protein in his sample. The standard protein returns absorbance values of 0.101, 0.204, 0.302, 0.405 for the respective quantities of 10ug, 20ug, 30ug, and 40ug of protein. The unknown sample returns an absorbance value of 0.265. What is the quantity of protein in the unknown sample?
A researcher performs a Bradford assay to determine the quantity of an unknown protein in his sample. The standard protein returns absorbance values of 0.101, 0.204, 0.302, 0.405 for the respective quantities of 10ug, 20ug, 30ug, and 40ug of protein. The unknown sample returns an absorbance value of 0.265. What is the quantity of protein in the unknown sample?
For this problem we need to determine the equation of our standard curve. This can be done by creating a graph from the data points and determining the slope.
Assuming that a sample of zero concentration will also have zero absorbance, we can find the equation for the line generated by finding the slope.
Pick two points on the line to find the slope. We will use (0,0) and (40,0.405).
Use this equation and the absorbance given in the question to find the concentration of the unknown sample.
For this problem we need to determine the equation of our standard curve. This can be done by creating a graph from the data points and determining the slope.
Assuming that a sample of zero concentration will also have zero absorbance, we can find the equation for the line generated by finding the slope.
Pick two points on the line to find the slope. We will use (0,0) and (40,0.405).
Use this equation and the absorbance given in the question to find the concentration of the unknown sample.
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Using the graph given, what is the value for the slope of the line?
Using the graph given, what is the value for the slope of the line?
The slope of the line, 
, can be calculated by the following equation:
The subscripts are simply the points you chose in the order you arbitrarily chose.The most important thing to do is plug the values into equation in the order you chose them.
To determine the slope of the line we need to use two points on the graph. Assuming the two points chosen correspond to 
and 
, plugging these values into the equation gives:
Therefore the slope of the line is equal to 
The slope of the line,
The subscripts are simply the points you chose in the order you arbitrarily chose.The most important thing to do is plug the values into equation in the order you chose them.
To determine the slope of the line we need to use two points on the graph. Assuming the two points chosen correspond to
Therefore the slope of the line is equal to
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Robert conducted an experiment in which he investigated how much water a paper towel could absorb. Initially, Robert found that one paper towel can absorb 12.8g of water. Later he found that his scale was not calibrated, so he had to repeat the experiment. After repeating the experiment with a new scale, Robert found that one paper towel can actually absorb 32.9g of water. What is the approximate percent error between the findings of the first and second experiments?
Robert conducted an experiment in which he investigated how much water a paper towel could absorb. Initially, Robert found that one paper towel can absorb 12.8g of water. Later he found that his scale was not calibrated, so he had to repeat the experiment. After repeating the experiment with a new scale, Robert found that one paper towel can actually absorb 32.9g of water. What is the approximate percent error between the findings of the first and second experiments?
The formula for percent error is:
In this case, the measured value is 12.8g and the accepted value is 32.9g.
The formula for percent error is:
In this case, the measured value is 12.8g and the accepted value is 32.9g.
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A reaction between one mole of sodium and one mole of chloride should yield 42 grams of sodium chloride. In your experiment, the actual yield is 32.73 grams. Calculate the percent error of your experiment.
A reaction between one mole of sodium and one mole of chloride should yield 42 grams of sodium chloride. In your experiment, the actual yield is 32.73 grams. Calculate the percent error of your experiment.
To find percent error we need to use the following equation:
Plug in 42 for the theoretical yield and 32.73 for the actual yield and solve accordingly.
To find percent error we need to use the following equation:
Plug in 42 for the theoretical yield and 32.73 for the actual yield and solve accordingly.
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In the following reaction, eight moles of sodium hydroxide is broken down into four moles of sodium oxide and four moles of water. What is the percent error if your experiment yields 195 grams of sodium oxide?
In the following reaction, eight moles of sodium hydroxide is broken down into four moles of sodium oxide and four moles of water. What is the percent error if your experiment yields 195 grams of sodium oxide?
To find the percent error we need to use the following equation:
But in order to do this, we first have to convert moles of sodium oxide into grams:
This gives us a theoretical yield of 248g, which we plug in with our 195g actual yield.
To find the percent error we need to use the following equation:
But in order to do this, we first have to convert moles of sodium oxide into grams:
This gives us a theoretical yield of 248g, which we plug in with our 195g actual yield.
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If a given sample of silver and flourine ideally combine to form 0.6mol of AgF, what is the percent error if the actual yield is 43 grams?
If a given sample of silver and flourine ideally combine to form 0.6mol of AgF, what is the percent error if the actual yield is 43 grams?
Our first step to complete this problem is to convert moles AgF into grams:
This gives us a theoretical yield of 76.2 grams. We can find the percent error by plugging in 76.2g for our theoretical yield and 43g for the actual yield in the following equation:
Our first step to complete this problem is to convert moles AgF into grams:
This gives us a theoretical yield of 76.2 grams. We can find the percent error by plugging in 76.2g for our theoretical yield and 43g for the actual yield in the following equation:
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Determine the percentage yield if the expected yield of 
in the above reaction is 40.911 grams but the actual yield is 35.322 grams.
Determine the percentage yield if the expected yield of
In chemistry, percentage yield is a term used to quantify the efficiency of a chemical reaction. In order to calculate this quantity, the value for the actual yield and theoretical yield is needed. The actual yield is the amount of product obtained during a chemical reaction. The theoretical yield is the maximum amount of product possible to be obtain by a chemical reaction which is based on the amount of reactants used. Below is the formula needed to calculate the percentage yield.
In chemistry, percentage yield is a term used to quantify the efficiency of a chemical reaction. In order to calculate this quantity, the value for the actual yield and theoretical yield is needed. The actual yield is the amount of product obtained during a chemical reaction. The theoretical yield is the maximum amount of product possible to be obtain by a chemical reaction which is based on the amount of reactants used. Below is the formula needed to calculate the percentage yield.
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0.0031 moles of 
was reacted with 0.0071 moles of 
giving an actual yield of 0.1733 grams of 
. What is the percent yield of this reaction?
0.0031 moles of
is the limiting reactant because based on the equation, 
and 
react in a 1:1 mole ratio. However, there is 0.0040 moles more of 
than 
present. Therefore the amount of 
produced is limited by the amount of 
present in the reaction. Based on the equation, for every 1 mole of 
reacted, 1 mole of 
was produced:
Therefore,
Therefore,
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Determine the percentage yield if the expected yield of 
in the above reaction is 1.2124 grams but the actual yield is 0.9749 grams.
Determine the percentage yield if the expected yield of
In chemistry, percentage yield is a term used to quantify the efficiency of a chemical reaction. In order to calculate this quantity, the value for the actual yield and theoretical yield is needed. The actual yield is the amount of product obtained during a chemical reaction. The theoretical yield is the maximum amount of product possible to be obtain by a chemical reaction which is based on the amount of reactants used. Below is the formula needed to calculate the percentage yield.
In chemistry, percentage yield is a term used to quantify the efficiency of a chemical reaction. In order to calculate this quantity, the value for the actual yield and theoretical yield is needed. The actual yield is the amount of product obtained during a chemical reaction. The theoretical yield is the maximum amount of product possible to be obtain by a chemical reaction which is based on the amount of reactants used. Below is the formula needed to calculate the percentage yield.
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Robert's work schedule for next week will be released today. Robert will work either 45, 40, 25, or 12 hours. The probabilities for each possibility are listed below:
45 hours: 0.3
40 hours: 0.2
25 hours: 0.4
12 hours: 0.1
What is the standard deviation of the possible outcomes?
Robert's work schedule for next week will be released today. Robert will work either 45, 40, 25, or 12 hours. The probabilities for each possibility are listed below:
45 hours: 0.3
40 hours: 0.2
25 hours: 0.4
12 hours: 0.1
What is the standard deviation of the possible outcomes?
There are four steps to finding the standard deviation of random variables. First, calculate the mean of the random variables. Second, for each value in the group (45, 40, 25, and 12), subtract the mean from each and multiply the result by the probability of that outcome occurring. Third, add the four results together. Fourth, find the square root of the result.
There are four steps to finding the standard deviation of random variables. First, calculate the mean of the random variables. Second, for each value in the group (45, 40, 25, and 12), subtract the mean from each and multiply the result by the probability of that outcome occurring. Third, add the four results together. Fourth, find the square root of the result.
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We have two independent, normally distributed random variables 
and 
such that 
has mean 
and variance 
and 
has mean 
and variance 
. What is the probability distribution of the difference of the random variables, 
?
We have two independent, normally distributed random variables
The mean for any set of random variables is additive in the sense that
The difference is also additive, so we have
This means the mean of 
is 
.
The variance is additive when the random variables are independent, which they are in this case. But it's additive in the sense that for any real numbers 
(even when negative), we have
.
So for this difference, we have
.
So the mean and variance are 
and 
, respectively. In addition to that, 
is normally distributed because the sum or difference of any set of independent normal random variables is also normally distributed.
The mean for any set of random variables is additive in the sense that
The difference is also additive, so we have
This means the mean of
The variance is additive when the random variables are independent, which they are in this case. But it's additive in the sense that for any real numbers
So for this difference, we have
So the mean and variance are
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47.0g of nitrous acid, HNO2, is added to 4L of water. What is the resulting pH? 
47.0g of nitrous acid, HNO2, is added to 4L of water. What is the resulting pH?
HNO2 is a weak acid; it will not fully dissociate, so we need to use the HA → H+ + A– reaction, with ![\dpi{100} \small K_{a}=\frac{\left [ products \right ]}{\left [ reactants \right ]}=\left \frac{\left [ H^{+} \right ]\left [ A^{-} \right ]}{\left [ HA \right ]}=4.1\times 10^{-4}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/18682/gif.latex)
.
47.0g HNO2 is equal to 1mol. 1mol into 4L gives a concentration of 0.25M when the acid is first dissolved; however, we want the pH at equilibrium, not at the initial state. As the acid dissolves, we know \[HNO2\] will decrease to become ions, but we don't know by how much so we indicate the decrease as "x". As HNO2 dissolves by a factor of x, the ion concentrations will increase by x.
HNO2 → H+ + NO2–
Initial 0.25M 0 0
Equilibrium 0.25 – x x x
Now, we can fill in our equation: ![\dpi{100} \small K_{a}=\left \frac{\left [ H^{+} \right ]\left [ A^{-} \right ]}{\left [ HA \right ]}=\frac{\left ( x \right )\left ( x \right )}{0.25-x}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/18683/gif.latex)
.
Since x is very small, we can ignore it in the denominator: 
(they expect you to do this on the MCAT; you will never have to solve with x in the denominator on the exam!)
Solve for x, and you find 
. Looking at our table, we know that ![\dpi{100} \small x=\left [ H^{+} \right ]](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/18686/gif.latex)
Now we can solve for pH: 
HNO2 is a weak acid; it will not fully dissociate, so we need to use the HA → H+ + A– reaction, with
47.0g HNO2 is equal to 1mol. 1mol into 4L gives a concentration of 0.25M when the acid is first dissolved; however, we want the pH at equilibrium, not at the initial state. As the acid dissolves, we know \[HNO2\] will decrease to become ions, but we don't know by how much so we indicate the decrease as "x". As HNO2 dissolves by a factor of x, the ion concentrations will increase by x.
HNO2 → H+ + NO2–
Initial 0.25M 0 0
Equilibrium 0.25 – x x x
Now, we can fill in our equation:
Since x is very small, we can ignore it in the denominator:
(they expect you to do this on the MCAT; you will never have to solve with x in the denominator on the exam!)
Solve for x, and you find
Now we can solve for pH:
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