Questions: What volume is occupied by a 0.792 mol sample of carbon dioxide gas at a temperature of 0°C and a pressure of 1 atm? L

Transcript text: What volume is occupied by a 0.792 mol sample of carbon dioxide gas at a temperature of $0^{\circ} \mathrm{C}$ and a pressure of 1 atm ? $\square$ L

Solution

Solution Steps

Step 1: Identify the Given Values

We are given:

Number of moles of CO$_2$ gas, $ n = 0.792 $ mol
Temperature, $ T = 0^{\circ} \mathrm{C} = 273.15 $ K
Pressure, $ P = 1 $ atm

Step 2: Use the Ideal Gas Law

The ideal gas law is given by: \[ PV = nRT \] where:

$ P $ is the pressure
$ V $ is the volume
$ n $ is the number of moles
$ R $ is the ideal gas constant, $ R = 0.0821 $ L·atm/(mol·K)
$ T $ is the temperature in Kelvin

Step 3: Solve for Volume

Rearrange the ideal gas law to solve for $ V $: \[ V = \frac{nRT}{P} \]

Step 4: Substitute the Given Values

Substitute the given values into the equation: \[ V = \frac{0.792 \, \text{mol} \times 0.0821 \, \text{L·atm/(mol·K)} \times 273.15 \, \text{K}}{1 \, \text{atm}} \]

Step 5: Calculate the Volume

Perform the calculation: \[ V = \frac{0.792 \times 0.0821 \times 273.15}{1} \] \[ V = 17.748 \, \text{L} \]