The volume of a gas is 93 mL when the temperature is 91°C. If the temperature is reduced to 0°C without changing the pressure, what is the new volume of the gas?
1 Answer
If we assume ideality, then we can use the ideal gas law:
#PV = nRT# where:
#P# is the pressure in#"bar"# , let's say.#V# is the volume in#"L"# .#n# is the number of#\mathbf("mol")# s of gas#R# is the universal gas constant, which will be, based on our units,#"0.083145 L"cdot"bar/mol"cdot"K"# .#T# is the temperature in units of#"K"# .
You can simply remember this equation instead of trying to remember all the smaller ones (Boyle's, Charles' and Gay-Lussac's laws, and Avogadro's Principle), and derive what you need.
We are looking at a change in volume due to a change in temperature, as stated in the question, and we assume that the pressure did NOT change.
Since
Then, suppose we solve for
#V_1 = (nRT_1)/P#
#V_2 = (nRT_2)/P#
Now, if we want to find
#V_2/V_1 = ((nRT_2)/P)/((nRT_1)/P) = T_2/T_1#
Therefore:
#color(blue)(V_2 = V_1 T_2/T_1#
So, you can use this formula to solve for
#color(blue)(V_2)#
#= "0.093 L" xx ("0 + 273.15 K"/"91 + 273.15 K")#
#~~# #color(blue)("0.070 L")#