Question #12ce4

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Answer 1 · 2017-05-26T20:27:28

The new pressure is 19.9 psi.

Given

The pressure ( $p_{1}$ $p_1$ ) of a gas at a temperature $T_{1}$ $T_1$ .
A second temperature $T_{2}$ $T_2$ .

Find

The second pressure $p_{2}$ $p_2$ .

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,

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

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