# 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 thepressurein#"bar"# , let's say.#V# is thevolumein#"L"# .#n# is thenumber of#\mathbf("mol")# sof gas#R# is theuniversal gas constant, which will be, based on our units,#"0.083145 L"cdot"bar/mol"cdot"K"# .#T# is thetemperaturein 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")#