Question

The pressure of a sample of gas at 10 oC increases from 700mmHg to 900mmHg. What is the new temperature?

a
0K
b
364K
c
91K
d
396K

Answer 1

To find the new temperature of the gas after the pressure change, you can use the ideal gas law, which states that for a gas at constant volume, the pressure is directly proportional to the temperature in Kelvin. The relationship can be expressed as:

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

Where:
- \(P_1\) = Initial pressure
- \(T_1\) = Initial temperature in Kelvin
- \(P_2\) = Final pressure
- \(T_2\) = Final temperature in Kelvin

First, we need to convert the initial temperature from degrees Celsius to Kelvin:

\[
T_1 = 10 \, \text{°C} + 273.15 = 283.15 \, \text{K}
\]

Now substituting the known values into the equation:

- \(P_1 = 700 \, \text{mmHg}\)
- \(T_1 = 283.15 \, \text{K}\)
- \(P_2 = 900 \, \text{mmHg}\)
- \(T_2 = ?\)

Now we can rearrange the formula to solve for \(T_2\):

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

Substituting the values:

\[
T_2 = \frac{900 \, \text{mmHg} \times 283.15 \, \text{K}}{700 \, \text{mmHg}}
\]

Calculating this gives:

\[
T_2 = \frac{900 \times 283.15}{700} \approx \frac{254835}{700} \approx 364.05 \, \text{K}
\]

Thus, the new temperature \(T_2\) is approximately **364K**.

So, the correct answer is **(b) 364K**.