AP Chemistry - Data Analysis and Other Calculations

Write the number 42,000,000 in scientific notation using the correct number of significant figures.

Explanation

The correct answer is . This is found by moving the decimal place to the left 7 times in order to get one digit to the left of the decimal, and the rest of the digits to the right. The answer just has two significant figures because that is the number of significant figures in the original number.

A student experimentally determines the specific heat of water to be $4.25 \frac{J}{g*K}$ . He then looks up the accepted value and finds that it is $4.18 \frac{J}{g*K}$ . What was the student's percent error?

Explanation

The formula for percent error is:

$\text{percent error} = \frac{|\text{accepted value - experimental value}|}{(\text{accepted value})} * 100$

Plug in the given values and solve:

$\frac{|4.18 - 4.25|}{(4.18)} * 100 = 1.67%$

Therefore, after accounting for significant figures the correct answer is

The hospital carries 0.9% $\left(\frac{w}{v}\right)$ solution of sodium chloride in purified $\small H_{2}O$ . The professor asked his student to prepare 500mL of 0.45% percent $\left(\frac{w}{v}\right)$ solution sodium chloride in purified $\small H_{2}O$ . What volumes of the original solution and purified , respectively, are needed to make the new solution?

$\small 250mL, 250mL$

$\small 200mL, 300mL$

$\small 400mL, 100mL$

$\small 225mL, 275mL$

Explanation

This is a typical dilution problem. The first step is to recognize that this is a dilution question. Whenever figuring out how to go from a higher concentrated solution to a lower concentrated solution, it is a dilution problem. The main equation to use here is:

$\small (Concentration_{1})$ $\small (Volume_{1})$ $\small = (Concentration_{2})(Volume_{2})$

$C_{1}V_{1} = C_{2}V_{2}$

$\small M_{1}V_{1}=M_{2}V_{2}$

When plugging in the numbers, make sure to assign the correct volumes and concentrations. Think of one side of the equation describing the 0.9% $\left(\frac{w}{v}\right)$ solution of sodium chloride and the other side describing the 0.45% solution of sodium chloride.

$0.45\cdot500=0.9\cdot V_2$

$\small V_{2}$ is the amount of the original solution needed to make the new 0.45% solution. However, we need to add water to the solution to dilute it. To find how much water is needed, subtract:

$\small 500mL - 250mL=250mL$ of water.

Solve and account for significant figures.

Calculate using the correct number of significant figures:

Explanation

The answer is 13.18 because the rules for adding and subtracting significant figures state that the answer can only be precise up to the least precise digit from the numbers that were added/subtracted. In this case 2.12 is only precise to the hundredth place, and therefore our answer can only go to the hundredth place.

Convert the number into standard notation, with the correct number of significant figures.

Explanation

To convert into standard notation we must move the decimal two places to the right because of the exponent of "2" above the 10. Then we re-write the number with the decimal in the new space. All of the digits that were in the original scientific notation must be accounted for. Thus, our answer must have six significant figures.

Table 1

The table shows the data obtained by three groups when finding the boiling point of methanol. The accepted value is $78.5^\circ C$ . Is group A precise, accurate or both?

Precise but not accurate

Precise and accurate

Accurate but not precise

Neither precise nor accurate

Explanation

Group A's values are precise because the data values are all close to each other, but it is not accurate because it none of them is near the accepted value.

Table 1

The table shows the data obtained by three groups when attempting to find the boiling point of methanol. The accepted value is $78.5^\circ C$ . Is group C precise, accurate, both, or neither?

Precise and accurate

Neither precise nor accurate

Accurate but not precise

Precise but not accurate

Explanation

Group C is precise because all of their values are close to one another. Their data is also accurate because their values are all near the accepted value. Therefore group C is both accurate and precise.

Find the volume that of carbon dioxide will occupy if it's density is $1.75 \frac{g}{mL}$ .

Explanation

Remember: $D = \frac{m}{V}$

Rearrange the equation to solve for volume:

$V = \frac{m}{D}$

Plug in the values given in the problem:

$V = \frac{36.9g}{(1.75 \frac{g}{mL})} = 21.0857 mL$

However, we must take into account significant figures. Because both our given values have 3 significant figures, our answer must have 3 significant figures.

Therefore after rounding the correct answer is:

How many significant figures does the number 42,000,000 have?

Explanation

42,000,000 has two significant figures because of the rule that states that trailing zeroes are never significant unless there is a decimal point. For example, if the number given was "42,000,000." it would be eight significant figures.

$Zn_{(s)}+2HCl_{(aq)}\rightarrow ZnCl_{2}_{(aq)}+H_{2}_{(g)}$

3.2 g Zn and 8.1 g HCl are placed in an open beaker. As the reaction proceeds, the hydrogen gas is allowed to escape, causing the reaction to go to completion.

Which reactant (if either) is in excess, and how many grams of it remain?

Neither reactant is in excess.

Explanation

First calculate the number of mols of each reactant:

$\frac{3.2 :g :Zn}{65.38:\frac{g :Zn}{mol :Zn}} = 0.048945 :mol :Zn$

$\frac{8.1 :g :HCl}{36.45:\frac{g :HCl}{mol :HCl}}=0.2222 :mol :HCl$

The ratio of to is 1:2. So, given that we have 0.048945 mol , we only need 0.09789 mol . Since we have more than is needed, is in excess. How much is in excess?