Question

A gas occupies 1676 mL at -85.1 °C and 225 mmHg. What will its temperature be when its volume is 838 mL at 3.5 atm?

Answer 1

The new temperature would be 839 °C.

Explanation:

To solve this problem, we can use the Combined Gas Laws:

`color(blue)(bar(ul(|color(white)(a/a)(p_1V_1)/T_1 = (p_2V_2)/T_2color(white)(a/a)|)))" "`

We can solve this equation for `T_2`.

`T_2 = T_1 × p_2/p_1 × V_2/V_1`

In this problem,

`p_1 = 225 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "0.2960 atm"; p_2 = "3.5 atm"`

`V_1 = "1676 mL";color(white)(mmmmmmmmmmmmmmmll) V_2 = "838 mL"`

`T_1 = "(-85.1 + 273.15) K = 188.05 K";color(white)(mmmmm) T_2 = ?`

∴ `T_2 = "188.05 K" × (3.5 color(red)(cancel(color(black)("atm"))))/(0.2960 color(red)(cancel(color(black)("atm")))) × (838 color(red)(cancel(color(black)("mL"))))/(1676 color(red)(cancel(color(black)("mL")))) = "1112 K" = "839 °C"`

The new temperature is 839 °C.