# Question #265c0

##### 1 Answer

Here's how you can do that.

#### Explanation:

Your starting point here will be the **ideal gas law equation**, which looks like this

#color(blue)(ul(color(black)(PV = nRT)))#

Here

#P# is the pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the sample#R# is theuniversal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is theabsolute temperatureof the gas

Now, let's say that the given mass of gas is **molar mass** of the gas, let's say

#n = m /M_M#

Plug this into the ideal gas law equation to get

#PV = m/M_M * RT#

Next, divide both sides of the equation by

#(PV)/T = m/M_M * R#

The molar mass of the gas, which tells you the mass of exactly **mole** of the gas, is **constant**.

#(PV)/T = overbrace(R/M_M)^(color(blue)("constant")) * m#

#(PV)/T = color(blue)("constant") * m#

This means that for a given mass **constant mass**, you can say that

#(PV)/T = color(blue)("constant")#

This is the **combined gas law equation** and it tells you that for a given mass of gas

#color(blue)(ul(color(black)((P_1V_1)/T_1 = (P_2V_2)/T_2)))#

Here

#P_1# ,#V_1# ,#T_1# are the pressure, volume, and absolute temperature of the gas at an initial state#P_2# ,#V_2# ,#T_2# are the pressure, volume, and absolute temperature of the gas at a final state