Question

question 12
one mole of a gas in a 1.0l closed container is heated from 20°c to 25°c. which equation below should be used to calculate the changed characteristic?
○ p₁v₁ = p₂v₂
○ p₁/t₁ = p₂/t₂
○ p₁/n₁ = p₂/n₂
○ v₁/t₁ = v₂/t₂

Explanation:

Step1: Analyze the given conditions

We have a gas in a closed container (so volume \( V \) is constant) with a fixed amount (1 mole, so amount of substance \( n \) is constant). The temperature \( T \) is changing from \( 20^\circ C \) to \( 25^\circ C \), and we need to find the equation for the changed characteristic (pressure \( P \) will change as temperature changes at constant \( V \) and \( n \)).

Step2: Recall gas laws

• Boyle's law: \( P_1V_1 = P_2V_2 \) (applies when \( T \) and \( n \) are constant, but here \( T \) is changing, so not applicable).
• Charles's law: \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \) (applies when \( P \) and \( n \) are constant, but here \( V \) is constant, so not applicable).
• Avogadro's law - related: \( \frac{P_1}{n_1}=\frac{P_2}{n_2} \) (applies when \( T \) and \( V \) are constant, but here we are changing \( T \), so not applicable).
• Gay - Lussac's law (Pressure - Temperature law): \( \frac{P_1}{T_1}=\frac{P_2}{T_2} \) (applies when \( V \) and \( n \) are constant, which matches our conditions: closed container (constant \( V \)) and 1 mole (constant \( n \)), temperature is changing, so pressure will change according to this law).

Answer:

\( \boldsymbol{\frac{P_1}{T_1}=\frac{P_2}{T_2}} \) (the second option in the given choices)