Question

question 10
the amount of gas in a 1.0l closed container is increased. which equation below should be
used to calculate the changed characteristic?
$\bigcirc p_1/t_1 = p_2/t_2$
$\bigcirc p_1v_1 = p_2v_2$
$\bigcirc p_1/n_1 = p_2/n_2$
$\bigcirc v_1/t_1 = v_2/t_2$

Explanation:

Step1: Analyze the problem conditions

The container is closed (volume \( V \) constant) and the amount of gas (\( n \)) is increased. We need to find the gas law that relates pressure (\( P \)) and amount of gas (\( n \)) when volume and temperature (assuming constant, as no info about temp change) are constant.

Step2: Recall gas laws

• \( \frac{P_1}{T_1}=\frac{P_2}{T_2} \): Relates pressure and temperature (constant \( V, n \)) - not for \( n \) change.
• \( P_1V_1 = P_2V_2 \): Relates pressure and volume (constant \( T, n \)) - not for \( n \) change.
• \( \frac{P_1}{n_1}=\frac{P_2}{n_2} \): From ideal gas law \( PV = nRT \), when \( V, T \) constant (\( R \) is constant), \( \frac{P}{n}=\text{constant} \), so this relates pressure and amount of gas (constant \( V, T \)) - matches the problem (closed container \( V = 1.0L \) constant, \( n \) increased).
• \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \): Relates volume and temperature (constant \( P, n \)) - not for \( n \) change.

Answer:

\( \boldsymbol{\frac{P_1}{n_1}=\frac{P_2}{n_2}} \) (the option with \( P_1/n_1 = P_2/n_2 \))