A mass of gas at 40mmHg is heated from 298k to 348k at constant volume. Cal the pressure exerted by the gas.

Analysis

This problem involves the relationship between the pressure and temperature of a fixed mass of gas when the volume is kept constant. This is governed by Gay-Lussac’s Law (also known as the Pressure Law).

Concept

Gay-Lussac’s Law states that for a fixed mass of gas at constant volume, the pressure ($P$) is directly proportional to its absolute temperature ($T$):

Where:

• $P_1$ = Initial pressure
• $T_1$ = Initial temperature
• $P_2$ = Final pressure
• $T_2$ = Final temperature

Solution

Step 1: Identify the given values

• $P_1 = 40 \text{ mmHg}$
• $T_1 = 298 \text{ K}$
• $T_2 = 348 \text{ K}$
• $P_2 = ?$

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

Step 3: Substitute the values into the equation

Rounding to two decimal places, we get 46.71 mmHg.

Conclusion

Comparing our result with the given options, the correct value is 46.71 mmHg.

Exam Tip

Always ensure your temperature is in Kelvin when using gas laws. If a question gives you temperature in Celsius, remember to add 273 to convert it to Kelvin before plugging it into your formula. Also, since pressure is directly proportional to temperature, if the temperature increases, your final pressure must be higher than the initial pressure. This helps you quickly eliminate impossible options!