# GRE Subject Test: Chemistry : Analytical Chemistry

## Example Questions

### Example Question #1 : Calibrations And Precision

What is the molar concentration of a 2% by mass  solution with a density of

Explanation:

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:

### Example Question #12 : Analytical Chemistry

Using the calibration curve given, if given the absorbance of 1.51, what would be the concentration?

Explanation:

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.

### Example Question #1 : Other Statistics

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.

Explanation:

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.

### Example Question #14 : Analytical Chemistry

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?

Explanation:

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,

### Example Question #2 : Other Statistics

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.

Explanation:

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.

### Example Question #1 : How To Find Standard Deviation Of A Random Variable

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?

Explanation:

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.

### Example Question #1 : How To Find Standard Deviation Of A Random Variable

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, ?

Normal distribution with mean  and variance .

Normal distribution with mean  and variance .

Normal distribution with mean  and variance .

Normal distribution with mean  and variance .

Normal distribution with mean  and variance .

Explanation:

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.

### Example Question #1 : Help With Quantification Techniques

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?

Explanation:

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.

### Example Question #11 : Analytical Chemistry

Using the graph given, what is the value for the slope of the line?

Explanation:

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

### Example Question #2 : Equilibrium Constant And Reaction Quotient

In the above reaction, by what factor would the reaction quotient change if the concentration of  were doubled?

No change