# AP Chemistry : Data Analysis and Other Calculations

## Example Questions

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### Example Question #1 : Data Analysis And Other Calculations

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:

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?

Now convert mols of  to grams:

### Example Question #1 : Laboratory Techniques And Analysis

25 mL of water at room temperature is vaporized and heated to 515 degrees Celsius in an open system.

What will the volume of the resulting gas be? Round your answer to the nearest liter.

Explanation:

The system is open, so the pressure can be assumed atmospheric, e.g. 1 atm.

Using the ideal gas law,

We need to convert  to kelvin.

The density of water at room temperature is approximately 1 g/mL, so we have 25 g of water. Convert to mols:

Plugging everything in:

### Example Question #1 : Calculations

A cylindrical metal wire, initially at 100 degrees Celsius, is immersed into a bomb calorimeter containing 100 mL of water at 25 degrees Celsius. After some time, the temperature of the system is homogenous at 35 degrees Celsius.

The wire is 135 cm long with a diameter of 0.1 cm.

What is the heat capacity of the metal? Round your answer to the nearest .

Explanation:

First we need to calculate the mass of the wire. We will do this by calculating its volume then multiplying by the density.

Next we need to find out how much energy the water gained from the metal wire.

The energy the water gained is equal to the energy the wire lost. This allows us to calculate the heat capacity for the metal:

### Example Question #4 : Data Analysis And Other Calculations

A chemistry student is trying to determine the identity of an unknown gas. If the gas has a molar mass of  at  and , what is the density of this unknown gas under these conditions?

Impossible to determine without additional information

Explanation:

We are given the pressure, temperature, and molar mass of the gas in the question stem and are asked to determine the density. To do this, we will need to make use of a manipulated form of the ideal gas equation.

To find density, we will need a way to relate the variables given in the question stem to other parameters, namely mass and volume. Since we already have the volume, , contained in the ideal gas equation, we just need a way to find the mass, . We can do this by noting that the number of moles, , can also be written as the mass divided by the molar mass, . Substituting this in gives us:

And rearranging, we obtain the density:

But we're not done yet! Remember, we also have to convert the units given for pressure and temperature in the question stem into their proper form. Since we need pressure in terms of atmospheres, and there are  in  of gas, we can find that:

Furthermore, we need to convert degrees Celsius into Kelvins.

Now that we have all the units in their correct form, we're finally ready to plug our values into the equation for density:

### Example Question #1 : Calculations

The hospital carries 0.9%  solution of sodium chloride in purified . The professor asked his student to prepare 500mL of 0.45% percent solution sodium chloride in purified . What volumes of the original solution and purified , respectively, are needed to make the new solution?

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:

or

or

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%  solution of sodium chloride and the other side describing the 0.45% solution of sodium chloride.

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:

of water.

### Example Question #181 : Ap Chemistry

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.

### Example Question #1 : Laboratory Techniques And Analysis

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.

### Example Question #182 : Ap Chemistry

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.

### Example Question #9 : Data Analysis And Other Calculations

Solve. Account for significant figures.

Calculate using the correct number of significant figures:

Explanation:

The answer is 500 because our rules of significant figures state that when two numbers are multiplied our answer can only have as many significant figures as our number with the fewest significant figures. In this case 5.02 has three significant figures, but 100 only has 1 significant figure. Therefore our answer can only have 1 significant figure.

### Example Question #2 : Data Analysis And Other Calculations

Solve and account for significant figures.

Calculate using the correct number of significant figures: