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?

We can solve this problem using the **ideal gas law** and the concept of **mole fraction**. Here’s how we can approach it:

### Step 1: Apply the Ideal Gas Law

The ideal gas law is:

\[
PV = nRT
\]

Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = total moles of gas (in moles)
- \( R \) = ideal gas constant = \( 0.0821 \, \text{L·atm/(mol·K)} \)
- \( T \) = temperature (in Kelvin)

We are given:
- Total pressure \( P = 1.02 \, \text{atm} \)
- Volume \( V = 0.75 \, \text{L} \)
- Temperature \( T = 273 \, \text{K} \)

Let's first calculate the total moles of gas (\( n_{\text{total}} \)) using the ideal gas law.

\[
n_{\text{total}} = \frac{PV}{RT} = \frac{1.02 \times 0.75}{0.0821 \times 273}
\]

### Step 2: Mole Fraction and Moles of NH₃

The mole fraction of hydrogen (\( X_{\text{H2}} \)) is given as 0.21. Since the total mole fraction must equal 1, the mole fraction of ammonia (\( X_{\text{NH3}} \)) is:

\[
X_{\text{NH3}} = 1 - X_{\text{H2}} = 1 - 0.21 = 0.79
\]

We can now use the mole fraction to find the moles of NH₃. The number of moles of NH₃ is:

\[
n_{\text{NH3}} = X_{\text{NH3}} \times n_{\text{total}}
\]

Let’s calculate the total moles of gas first and then the moles of NH₃.

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 of H2 and NH3 using the ideal gas law and mole fraction. The problem involves key chemistry concepts like PV = nRT and mole fraction determination, suitable for college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation