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This question involves the behavior of ammonia gas treated as an ideal gas, so we can use the ideal gas law to analyze the situation:

\[
PV = nRT
\]

Where:
- \( P \) = pressure,
- \( V \) = volume,
- \( n \) = number of moles (constant in this case),
- \( R \) = ideal gas constant (constant),
- \( T \) = temperature (in Kelvin).

To see how the volume \( V \) changes, let's focus on the relationship between pressure, temperature, and volume. We assume that the number of moles and the gas constant remain constant, giving us:

\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]

Rearranging to solve for the change in volume:

\[
V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1}
\]

### Data from the problem:
- Initial temperature \( T_1 = 55.0^\circ C = 55 + 273.15 = 328.15 \, K \)
- Final temperature \( T_2 = 71.0^\circ C = 71 + 273.15 = 344.15 \, K \)
- Initial pressure \( P_1 \) is not given explicitly, but the final pressure \( P_2 \) is 15% higher, so \( P_2 = 1.15 \times P_1 \).

Now let's calculate the change in volume:

\[
V_2 = V_1 \times \frac{P_1}{1.15 P_1} \times \frac{344.15}{328.15}
\]

The \( P_1 \) terms cancel out:

\[
V_2 = V_1 \times \frac{344.15}{1.15 \times 328.15}
\]

Simplifying:

\[
V_2 = V_1 \times \frac{344.15}{377.37} = V_1 \times 0.912
\]

This shows that the volume decreases by approximately 8.8%.

### Answer:
- The volume **decreases**.
- The percentage decrease in volume is about **9%** (rounded to the nearest percent).

Would you like any additional details or have questions? Here are some related questions:

1. What assumptions are made in using the ideal gas law for this problem?
2. How would the result change if the pressure increase was only 10%?
3. What if the temperature change was more drastic, say from 55°C to 100°C?
4. How is the behavior of real gases different from ideal gases?
5. How would the volume change if both pressure and temperature were doubled?

**Tip**: Always convert temperatures to Kelvin when working with the ideal gas law!

Suppose the temperature of a sample of ammonia gas is raised from 55.0°C to 71.0°C, and at the same time the pressure is increased by 15.0%. Does the volume of the sample increase, decrease, or stay the same? If it changes, calculate the percentage change in the volume.

Analyze the volume change of ammonia gas when the temperature rises from 55°C to 71°C and the pressure increases by 15%. Learn how to calculate percentage change in gas volume using the ideal gas law. Suitable for high school students studying chemistry or physics.

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