# Which flask contains gas of molar mass 30, and which contains gas of molar mass 60?

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Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30, the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is X kPa, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5 X kPa, and the mass of gas in that flask is 1.2 g.

Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30, the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is X kPa, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5 X kPa, and the mass of gas in that flask is 1.2 g.

##### 1 Answer

Here's what I got.

#### Explanation:

**!! QUICK ANSWER !!**

The trick here is to realize that

pressureisdirectly proportionalto the number ofmolesof gas present in each flaskthe number of moles isinversely proportionalto themolar massof the gas

Pressure is directly proportional to the number of moles of gas, which means that a pressure that is **twice as high** corresponds to **twice as many** moles of gas present in the flask.

Therefore, flask A contains **twice as many** moles of gas as flask B. Now, the **heavier gas** will contain **fewer moles** in the **same mass**.

The two samples have the same mass, but flask A contains twice as many moles as flask B, which can only mean that the gas present in flask A has a molar mass of

Therefore,

#"Flask A " -> " 30 g mol"^(-1)#

#"Flask B " -> " 60 g mol"^(-1)#

**!! DETAILED EXPLANATION !!**

The problem tells you that the two flasks have the **same volume**, let's say **same temperature**, let's say

This means that if you start from the **ideal gas law** equation

where

#P# - the pressure of the gas

#V# - the volume it occupies

#n# - the number of moles of gas

#R# - theuniversal gas constant

#T# - theabsolute temperatureof the gas

you can say that you have

#P_A * V = n_A * R * T -># for the gas present inflask A

#P_b * V = n_B * R * T -># for the gas present inflask B

Divide these two equations to find a relationship between the pressure of the two gases and the number of moles of gas present in each flask

#(P_A * color(red)(cancel(color(black)(V))))/(P_B * color(red)(cancel(color(black)(V)))) = (N_A * color(red)(cancel(color(black)(R))) * color(red)(cancel(color(black)(T))))/(n_B * color(red)(cancel(color(black)(R))) * color(red)(cancel(color(black)(T)))) implies P_A/P_B = n_A/n_B#

Now, you know that the pressure in **flask A**, given as **twice as high** as the pressure in **flask B**, given as

This means that the ratio between the number of moles of gas present in each flask will be

#(color(red)(cancel(color(black)("X")))color(red)(cancel(color(black)("kPa"))))/(1/2 * color(red)(cancel(color(black)("X"))) color(red)(cancel(color(black)("kPa")))) = n_A/n_B implies n_A/n_B =2#

This is equivalent to

#color(purple)(|bar(ul(color(white)(a/a)color(black)(n_A = 2 * n_B)color(white)(a/a)|)))" " " "color(orange)("(*)")#

You now know that flask A contains **twice as many moles** of gas as flask B.

Now, you know that the two gases have **the same mass**, given as **twice as big** as the molar mass of the gas present in flask A, let's say

This is the case because

#n_A = (1.2 color(red)(cancel(color(black)("g"))) )/(M_A color(red)(cancel(color(black)("g"))) "mol"^(-1)) = 1.2/M_Acolor(white)(a)"moles"#

#n_B = (1.2 color(red)(cancel(color(black)("g"))))/(M_B color(red)(cancel(color(black)("g"))) "mol"^(-1)) = 1.2/M_B color(white)(a)"moles"#

According to equation

#color(red)(cancel(color(black)(1.2)))/M_A = 2 * color(red)(cancel(color(black)(1.2)))/M_B implies color(green)(|bar(ul(color(white)(a/a)color(black)(M_B = 2 * M_A)color(white)(a/a)|)))#

This means that flask A contains the gas with the molar mass of

Once again,

#"Flask A " -> " 30 g mol"^(-1)#

#"Flask B " -> " 60 g mol"^(-1)#