A Mixture of H2 an NH3 has a total pressure of 1.02 atm at 273k in a 0.75l container. If H2 is present in a mole fraction of 0.21, how many moles of NH3 are present?

To determine how many moles of \( NH_3 \) are present, we can use the ideal gas law and the given information about the mole fraction.

The ideal gas law is:

\[
PV = nRT
\]

Where:
- \( P \) is the total pressure (1.02 atm),
- \( V \) is the volume of the container (0.75 L),
- \( n \) is the total number of moles of the gas mixture,
- \( R \) is the ideal gas constant (0.0821 L·atm/(mol·K)),
- \( T \) is the temperature (273 K).

### Step 1: Calculate the total number of moles of gas in the mixture
Using the ideal gas law:

\[
n = \frac{PV}{RT}
\]

Substitute the known values:

\[
n = \frac{1.02 \, \text{atm} \times 0.75 \, \text{L}}{0.0821 \, \text{L·atm/(mol·K)} \times 273 \, \text{K}}
\]

Let's calculate that.

The total number of moles of gas in the mixture is approximately \( 0.0341 \, \text{moles} \).

### Step 2: Calculate the moles of \( H_2 \)
The mole fraction of \( H_2 \) is given as \( 0.21 \), so the number of moles of \( H_2 \) can be calculated as:

\[
n_{\text{H}_2} = \text{mole fraction of H}_2 \times n_{\text{total}}
\]

Substitute the values:

\[
n_{\text{H}_2} = 0.21 \times 0.0341
\]

Let's calculate that.The number of moles of \( H_2 \) is approximately \( 0.00717 \, \text{moles} \).

### Step 3: Calculate the moles of \( NH_3 \)
The moles of \( NH_3 \) can be found by subtracting the moles of \( H_2 \) from the total number of moles:

\[
n_{\text{NH}_3} = n_{\text{total}} - n_{\text{H}_2}
\]

Substitute the values:

\[
n_{\text{NH}_3} = 0.0341 - 0.00717
\]

Let's calculate that.The number of moles of \( NH_3 \) present is approximately \( 0.02696 \, \text{moles} \).

Would you like a more detailed explanation or any further clarifications? Here are five related questions to explore this topic further:

1. How does the ideal gas law apply to mixtures of gases?
2. What would happen if the mole fraction of \( H_2 \) increased?
3. How would the total pressure change if the temperature were raised to 300 K?
4. What is the significance of the mole fraction in gas mixtures?
5. How would the volume of the container affect the number of moles?

**Tip**: Mole fraction is a useful way to express the ratio of one gas in a mixture, as it simplifies calculations for determining individual gas contributions.

A Mixture of H2 and NH3 has a total pressure of 1.02 atm at 273k in a 0.75l container. If H2 is present in a mole fraction of 0.21, how many moles of NH3 are present?

Learn how to calculate the moles of NH3 in a gas mixture with a total pressure of 1.02 atm, given the mole fraction of H2 is 0.21. This problem involves the Ideal Gas Law and mole fractions, providing a detailed step-by-step solution. Suitable for students in Grades 10-12.

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