A gas mixture contains 1.05 g N2 and 1.53 g O2 in a 1.47-L container at 21 ∘C. Calculate partial pressure of N2 gas mixture

To calculate the partial pressure of nitrogen (\(N_2\)) in the gas mixture, we will use the **ideal gas law** equation:

\[
PV = nRT
\]

Where:
- \(P\) is the pressure (which we need to find),
- \(V\) is the volume of the container (1.47 L),
- \(n\) is the number of moles of \(N_2\),
- \(R\) is the ideal gas constant \((0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})\),
- \(T\) is the temperature in Kelvin.

### Step 1: Convert temperature from Celsius to Kelvin
\[
T = 21^\circ C + 273.15 = 294.15 \, K
\]

### Step 2: Calculate the moles of \(N_2\)
The molar mass of nitrogen (\(N_2\)) is:
\[
\text{Molar mass of } N_2 = 28.02 \, \text{g/mol}
\]

The number of moles of \(N_2\) is:
\[
n = \frac{1.05 \, \text{g}}{28.02 \, \text{g/mol}} \approx 0.0375 \, \text{mol}
\]

### Step 3: Apply the ideal gas law for \(N_2\)
Rearrange the ideal gas law to solve for \(P\):

\[
P = \frac{nRT}{V}
\]

Substitute the known values:

\[
P = \frac{(0.0375 \, \text{mol}) (0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}) (294.15 \, \text{K})}{1.47 \, \text{L}}
\]

Now, let's calculate the partial pressure of \(N_2\).The partial pressure of nitrogen (\(N_2\)) in the gas mixture is approximately **0.616 atm**.

Do you want more details on the steps? 

Here are 5 related questions you might find useful:
1. How is the partial pressure of oxygen (\(O_2\)) in the same mixture calculated?
2. What is the total pressure in the container?
3. How do real gases deviate from the ideal gas law?
4. How does temperature affect the pressure of a gas?
5. What is Dalton's Law of Partial Pressures?

**Tip:** Always ensure temperature is in Kelvin when using the ideal gas law to avoid calculation errors.

A gas mixture contains 1.05 g N2 and 1.53 g O2 in a 1.47-L container at 21 ∘C. Calculate the partial pressure of N2 gas mixture.

Learn how to calculate the partial pressure of nitrogen (N2) in a gas mixture using the ideal gas law. This example covers the ideal gas law formula, moles of nitrogen, and temperature conversion from Celsius to Kelvin. Suitable for high school students studying chemistry.

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