# A sample of 25 L of NH_3 gas at 10°C is heated at constant pressure until it fills a volume of 50 L. What is the new temperature in °C?

Aug 9, 2017

$293$ $\text{^"o""C}$

#### Explanation:

We're asked to find the new temperature of the ${\text{NH}}_{3}$ after it is subdued to a change in volume (with constant pressure).

To do this, we can use the temperature-volume relationship of gases, illustrated by Charles's law:

$\underline{\overline{| \stackrel{\text{ ")(" "(V_1)/(T_1) = (V_2)/(T_2)" }}{|}}}$ $\text{ }$(constant pressure and quantity of gas)

where

• ${V}_{1}$ and ${V}_{2}$ are the initial and final volumes of the gas

• ${T}_{1}$ and ${T}_{2}$ are the initial and final absolute temperatures of the gas (which must be in Kelvin)

We have:

• ${V}_{1} = 25$ $\text{L}$

• ${V}_{2} = 50$ $\text{L}$

• ${T}_{1} = 10$ $\text{^"o""C" +273 = ul(283color(white)(l)"K}$

• T_2 = ?

Let's rearrange the above equation to solve for the final temperature, ${T}_{2}$:

${T}_{2} = \frac{{V}_{2} {T}_{1}}{{V}_{1}}$

Plugging in known values:

T_2 = ((50cancel("L"))(283color(white)(l)"K"))/(25cancel("L")) = color(red)(ul(566color(white)(l)"K"

You asked for the temperature in degrees Celsius, so we convert back:

color(red)(566color(white)(l)"K") - 273 = color(blue)(ulbar(|stackrel(" ")(" "293color(white)(l)""^"o""C"" ")|)