A sample of 25 L of $N H_{3}$ $NH_3$ gas at 10°C is heated at constant pressure until it fills a volume of 50 L. What is the new temperature in °C?

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Answer 1 · 2017-08-09T03:11:16

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

We're asked to find the new temperature of the ${NH}_{3}$ $"NH"_3$ 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:

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:

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

A sample of 25 L of NH_3NH3NH_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?