The problem involves nitrogen gas (N₂) being treated as an ideal gas. The temperature is raised from 73.0 °C to 108.0 °C, and at the same time, the pressure is decreased by 15.0%. We need to determine:

1. Does the volume increase, decrease, or stay the same?
2. If there is a change in volume, calculate the percentage change.

Step 1: Ideal Gas Law

The ideal gas law equation is:

$PV = nRT$

Where:

• $P$ is pressure,
• $V$ is volume,
• $n$ is the number of moles,
• $R$ is the gas constant,
• $T$ is temperature in Kelvin.

To analyze how volume changes, we can rewrite this equation as:

$V = \frac{nRT}{P}$

From this, we can see that volume is directly proportional to temperature ($T$) and inversely proportional to pressure ($P$).

Step 2: Convert Temperatures to Kelvin

• Initial temperature: T_1 = 73.0 \,^\circ\text{C} = 73 + 273.15 = 346.15 \, \text{K}
• Final temperature: T_2 = 108.0 \,^\circ\text{C} = 108 + 273.15 = 381.15 \, \text{K}

Step 3: Percentage Change in Pressure

The pressure is decreased by 15%, so the final pressure $P_2$ is 85% of the initial pressure $P_1$:

$P_2 = 0.85 P_1$

Step 4: Calculate Volume Change

The ratio of the final volume to the initial volume is given by:

$\frac{V_2}{V_1} = \frac{\frac{nRT_2}{P_2}}{\frac{nRT_1}{P_1}} = \frac{T_2}{T_1} \times \frac{P_1}{P_2}$

Substitute the values for temperature and pressure:

$\frac{V_2}{V_1} = \frac{381.15}{346.15} \times \frac{P_1}{0.85 P_1} = \frac{381.15}{346.15} \times \frac{1}{0.85}$

Now let's calculate this.The ratio of the final volume $V_2$ to the initial volume $V_1$ is approximately 1.295. This means the volume increases by about 29.5%.

Final Answer:

• The volume increases.
• The percentage increase in volume is approximately 30% (rounded to the nearest percent).

Would you like further details or clarifications?

Related Questions:

1. How does the ideal gas law explain the relationship between pressure, volume, and temperature?
2. What would happen to the volume if the pressure decreased by 20% instead of 15%?
3. How would the outcome change if the gas were cooled instead of heated?
4. How do real gases deviate from the ideal gas law at low temperatures?
5. Can the ideal gas law be applied at very high pressures and low temperatures?

Tip:

Always ensure to convert temperatures to Kelvin when using the ideal gas law!