# Gas Law Problems: Calculating Pressure, Volume, and Temperature

## Problem 1:

**1.37 mol**sample of nitrogen gas at a temperature of

**29.0 ∘ C**is found to occupy a volume of

**21.4 liters**. The pressure of this gas sample is mmHg.

## Problem 2:

A sample of xenon gas collected at a pressure of**791 mmHg**and a temperature of

**287 K**has a mass of

**144 grams**. The volume of the sample is L.

## Problem 3:

A**8.58 gram**sample of carbon dioxide gas has a volume of

**951 milliliters**at a pressure of

**3.50 atm**. The temperature of the CO

_{2}gas sample is ∘ C. What are the pressure of the nitrogen gas, volume of the xenon gas, and temperature of the carbon dioxide gas sample?

### Final answer:

The questions are solved by applying the **ideal gas law** equation, PV = nRT, and adjusting to solve for the variable in question. The pressure of nitrogen gas, volume of Xenon, and temperature of CO_{2} are calculated by substituting the given values into the rearranged **equations**.

### Explanation:

To answer this question, we need to apply the ideal gas law equation: PV=nRT. In this equation, P represents pressure, V stands for volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

For the nitrogen gas question, the temperature must be converted from Celsius to Kelvin first, which results in 302K. The ideal gas law can now be rearranged to solve for pressure: P= nRT/V. Substituting the given values of n, R (using 0.0821 L.atm/(mol.K), convert the volume from L to atm), T, and V, we can find the pressure.

In the second question concerning xenon gas, the molar mass of Xenon (131 g/mol) is used to calculate the number of moles. Applying the same steps as above, we can then determine the volume.

For the CO_{2}, we're solving for temperature, which requires rearranging the ideal gas law to T = PV/nR. After converting the given values into appropriate units, we can calculate the temperature.