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?
1 Answer
Explanation:
We're asked to find the new temperature of the
To do this, we can use the temperaturevolume 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 = (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"" "))#