200 cm3 of a gas at 25ºC exerts a pressure of 700 mmHg. Calculate its pressure if its volume increase 350 cm3 at 75ºC.

Analysis

This problem involves the behavior of a fixed mass of gas under changing conditions of pressure, volume, and temperature. To solve this, we use the General Gas Law (also known as the Combined Gas Law).

Concept

The Combined Gas Law states that for a fixed amount of gas:

Where:

• $P_1, V_1, T_1$ are the initial pressure, volume, and temperature.
• $P_2, V_2, T_2$ are the final pressure, volume, and temperature.

Important Note: In gas law calculations, temperature must always be converted from Celsius (°C) to Kelvin (K) by adding 273.15 (or 273 for JAMB purposes).

Step-by-Step Solution

1. Identify the given values:

• $P_1 = 700 \text{ mmHg}$
• $V_1 = 200 \text{ cm}^3$
• $T_1 = 25^\circ\text{C} = 25 + 273 = 298 \text{ K}$
• $V_2 = 350 \text{ cm}^3$
• $T_2 = 75^\circ\text{C} = 75 + 273 = 348 \text{ K}$
• $P_2 = ?$

2. Rearrange the formula to solve for $P_2$:

3. Substitute the values into the equation:

4. Perform the calculation:

• Numerator: $700 \times 200 \times 348 = 48,720,000$
• Denominator: $350 \times 298 = 104,300$
• $P_2 = \frac{48,720,000}{104,300} \approx 467.114 \text{ mmHg}$

Rounding to two decimal places, we get 467.11 mmHg.

Conclusion

Comparing our result with the given options, the correct value is 467.11 mmHg.

Exam Tip

Always remember to convert your temperature to Kelvin! A common mistake students make in JAMB is using the temperature in Celsius directly, which will lead to an incorrect answer. Also, check your units—since the pressure is requested in mmHg and the initial pressure is in mmHg, no unit conversion is needed for pressure.