Question

There are two containers filled with gases.In both containers,gases are same temperature and pressure.The first container is 3 L and contains 0.9 moles of gases.The second container is 1 L.How many moles of gas are there in the second container?

Accepted Answer

To solve for the number of moles of gas in the second container, apply Ideal Gas Law. The formula is:
PV = nRT
where P - pressure , V - volume , T - temperature, n -  number of moles and R - universal constant (R=8.3145J / mol K ).
The given in the first conatiner are V = 3L and n=9 moles. Substitute these to the formula above.
P_1(3) = 0.9 (8.3145)T_1
Then, isolate P_1 and T_1 since their values are unknown.
P_1/T_1 = (0.9(8.3145))/3
P_1/T_1 = 2.49435
And in the second container, the given is V=1 L. Substitute this to the formula of Ideal Gas Law.
P_2(1)=n(8.3145)T_2
Isolate P_2 and T_2 too.
P_2/T_2 = (8.3145n)/1
P_2/T_2 = 8.3145n
Note that the pressure and temperature of the gases inside the two containers are the same. So,
P_1/T_1 = P_2/T_2
2.49435=8.3145n
Then divide both sides by 8.3145 to solve for n.
2.49435/8.3145=(8.3145n)/8.3145
n =0.3
Hence, there are 0.3 moles of gases in the second container.

Answer

This can be done by ideal gas law PV = nRT.
Let;
n1 = moles in gas 1 = 0.9
n2 = moles in gas 2
 
R = 8.314 
V1 = 3L 
V2 = 1L 
 
For both cases pressure and temperature is same.And R is also same for both gases.
PV = nRT 
P/(RT) = n/V 
Since P/(RT) is same for both;
(n1)/(V1) = (n2)/(V2) 
n2 = (n1V2)/(V1) 
n2 = 0.9*1/3 
n2 = 0.3 
 
So in the other gas there are 0.3 moles.
 
Assumption
Both gasses act as ideal gasses.

Science Questions and Answers

There are two containers filled with gases.In both containers,gases are same temperature and pressure.The first container is 3 L and contains 0.9 moles of gases. The second container is 1 L.How many moles of gas are there in the second container?

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