Chemistry Regents Practice Test

Which temperature change would cause a sample of an ideal gas to double in volume while the pressure is held constant?

1. From 100K to 200K

2. From 200K to 400K

3. From 150K to 300K

4. From 300K to 600K

The correct answer is: From 200K to 400K

In this scenario, we can use Charles's Law, which states that for a given amount of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature (measured in Kelvin). Mathematically, Charles's Law can be expressed as: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Where \( V_1 \) and \( T_1 \) are the initial volume and temperature, and \( V_2 \) and \( T_2 \) are the final volume and temperature. For the volume to double, the final volume \( V_2 \) must be twice the initial volume \( V_1 \). We can set up the equation as follows: \[ \frac{V_1}{T_1} = \frac{2V_1}{T_2} \] When we simplify this, we see that: \[ T_2 = 2T_1 \] This shows that to double the volume while keeping pressure constant, the final temperature must be twice the initial temperature. Now let’s analyze the specific temperature changes provided: - From 100K to 200