Math Snap

STEP 1

1. We are given the moles of nitrogen gas and methane gas.
2. The volume of the container is 171.6 ml.
3. The temperature is given as $20.8^{\circ} \mathrm{C}$.
4. We need to find the partial pressure of nitrogen gas in atm.
5. We will use the ideal gas law to find the partial pressure.

STEP 2

1. Convert the volume from ml to liters.
2. Convert the temperature from Celsius to Kelvin.
3. Use the ideal gas law to calculate the partial pressure of nitrogen gas.

STEP 3

Convert the volume from ml to liters.
$$\text{Volume in liters} = \frac{171.6 \, \text{ml}}{1000} = 0.1716 \, \text{L}$$

STEP 4

Convert the temperature from Celsius to Kelvin.
$$\text{Temperature in Kelvin} = 20.8 + 273.15 = 293.95 \, \text{K}$$

Use the ideal gas law to calculate the partial pressure of nitrogen gas. 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 ($0.0821 \, \text{L atm/mol K}$),
- $T$ is the temperature in Kelvin.
Rearrange the formula to solve for $P$:
$$P = \frac{nRT}{V}$$ Substitute the values for nitrogen gas:
$$P = \frac{0.7515 \, \text{moles} \times 0.0821 \, \text{L atm/mol K} \times 293.95 \, \text{K}}{0.1716 \, \text{L}}$$ Calculate the partial pressure:
$$P = \frac{0.7515 \times 0.0821 \times 293.95}{0.1716}$$ $$P \approx \frac{18.108}{0.1716}$$ $$P \approx 105.55 \, \text{atm}$$ The closest answer choice is:
$\boxed{106}$