Question

Question #12ce4

Answer 1

The new pressure is 19.9 psi.

Explanation:

Given

The pressure (`p_1`) of a gas at a temperature `T_1`.
A second temperature `T_2`.

Find

The second pressure `p_2`.

Strategy

A problem involving two gas pressures and two temperatures must be a Gay-Lussac's Law problem.

Gay-Lussac's Law is

`color(blue)(bar(ul(|color(white)(a/a)p_1/T_1 = p_2/T_2color(white)(a/a)|)))" "`

1. Solve the Gay-Lussac's Law expression for `p_2`.

2. Insert the numbers into the `p_2` expression.

Solution

`p_2 = p_1 × T_2/T_1`

In your problem,

`p_1 = "22.5 psi"; T_1 = "(110 + 273.15K)" = "383.15 K"`
`p_2 = ?; color(white)(mmm)T_2 = "(65 + 273.15 K)" = "338.15 K"`

`p_2 = "22.5 psi" × (338.15 cancel("K"))/(383.15 cancel("K")) = "19.9 psi"`