Question

A 3.0 L container holds a sample of hydrogen gas at 300 K and 100 kPa. If the pressure increases to 400 kPa, and the volume remains constant, what will the temperature be?

Responses:
a) 600 K
b) 900 K
c) 1,200 K
d) 1,500 K

Answer 1

Using Gay-Lussac's Law, which shows that pressure and temperature are directly proportional at constant volume, the final temperature of the hydrogen gas when the pressure increases from 100 kPa to 400 kPa at a constant volume is 1200 K. This corresponds to option (c) in the multiple choice answers.

Step-by-step explanation:

The question concerns the behavior of a gas under constant volume when the pressure changes, and we want to find the resulting temperature. To solve this, we apply Gay-Lussac's Law from chemistry, which states that for a given mass of gas at a constant volume, the pressure is directly proportional to its absolute temperature. The law is represented by the formula P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 the final pressure and temperature respectively.

Given the initial conditions of hydrogen gas at 300 K and 100 kPa (P1 and T1), and the final pressure of 400 kPa (P2), we need to find the final temperature (T2). Using the formula, we can solve for T2 by rearranging it to T2 = (P2 * T1) / P1. Plugging in the values, we get T2 = (400 kPa * 300 K) / 100 kPa, which simplifies to T2 = 1200 K.

Therefore, the final temperature of the hydrogen gas when the pressure increases to 400 kPa and the volume stays the same is 1200 K, which corresponds to option (c).