Question

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?

Answer 1

`293` `""^"o""C"`

Explanation:

We're asked to find the new temperature of the `"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:

`ulbar(|stackrel(" ")(" "(V_1)/(T_1) = (V_2)/(T_2)" ")|)` `" "`(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` `"L"`

• `V_2 = 50` `"L"`

• `T_1 = 10` `""^"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 = (V_2T_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"" ")|)`