Mg3N2 + 3H2O ––> 3 MgO + 2NH3

If 10.3 g of magnesium nitride is used, what volume of ammonia gas would be collected at 20˚C and 0.989 atm?

To solve this, we will approach it step by step. 

### Step 1: Write the balanced equation:
The balanced chemical equation is:

\[
\text{Mg}_3\text{N}_2 + 3\text{H}_2\text{O} \longrightarrow 3\text{MgO} + 2\text{NH}_3
\]

### Step 2: Calculate the moles of \( \text{Mg}_3\text{N}_2 \):
We are given that \( 10.3 \, \text{g} \) of magnesium nitride (\( \text{Mg}_3\text{N}_2 \)) is used. First, we need to calculate the molar mass of \( \text{Mg}_3\text{N}_2 \).

- Molar mass of magnesium (Mg) = \( 24.305 \, \text{g/mol} \)
- Molar mass of nitrogen (N) = \( 14.007 \, \text{g/mol} \)

\[
\text{Molar mass of } \text{Mg}_3\text{N}_2 = 3 \times 24.305 + 2 \times 14.007 = 72.915 + 28.014 = 100.929 \, \text{g/mol}
\]

Now, calculate the moles of \( \text{Mg}_3\text{N}_2 \):

\[
\text{Moles of } \text{Mg}_3\text{N}_2 = \frac{10.3 \, \text{g}}{100.929 \, \text{g/mol}} = 0.1021 \, \text{mol}
\]

### Step 3: Determine the moles of \( \text{NH}_3 \) produced:
From the balanced equation, we see that 1 mole of \( \text{Mg}_3\text{N}_2 \) produces 2 moles of ammonia \( \text{NH}_3 \).

\[
\text{Moles of } \text{NH}_3 = 0.1021 \, \text{mol} \times \frac{2 \, \text{mol NH}_3}{1 \, \text{mol Mg}_3\text{N}_2} = 0.2042 \, \text{mol NH}_3
\]

### Step 4: Use the ideal gas law to calculate the volume of ammonia:
The ideal gas law is:

\[
PV = nRT
\]

Where:
- \( P = 0.989 \, \text{atm} \) (given)
- \( V \) is the volume (what we want to find)
- \( n = 0.2042 \, \text{mol NH}_3 \) (calculated)
- \( R = 0.0821 \, \text{L·atm/mol·K} \) (ideal gas constant)
- \( T = 20^\circ \text{C} = 293.15 \, \text{K} \)

Solving for \( V \):

\[
V = \frac{nRT}{P} = \frac{0.2042 \, \text{mol} \times 0.0821 \, \text{L·atm/mol·K} \times 293.15 \, \text{K}}{0.989 \, \text{atm}}
\]

\[
V = \frac{4.919}{0.989} = 4.974 \, \text{L}
\]

### Final Answer:
The volume of ammonia gas collected is approximately \( \boxed{4.97 \, \text{L}} \).

---

Would you like more details or clarifications? Here are some related questions you might find helpful:

1. What is the effect of temperature on gas volume according to the ideal gas law?
2. How would changing the pressure affect the volume of ammonia gas collected?
3. How does the stoichiometry of a chemical reaction help in calculating product amounts?
4. What assumptions are made in the ideal gas law?
5. How does real gas behavior differ from ideal gas predictions at high pressures?

**Tip:** Always check that the units in your gas law calculations are consistent—especially temperature, which must always be in Kelvin.

If 10.3 g of magnesium nitride is used, what volume of ammonia gas would be collected at 20˚C and 0.989 atm?

Find out how to calculate the volume of ammonia gas collected when 10.3 g of magnesium nitride reacts with water at 20˚C and 0.989 atm. Learn how to apply stoichiometry and the ideal gas law in this detailed step-by-step solution. Suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation