Question

Assuming constant pressure and temperature, how many moles of gas have been added to the initial 3 moles of gas when the volume increases from 2.0 to 4.0 liters?
1.5 moles

2 moles

3 moles

6 moles

Answer 1

We first assume that the gas is ideal which is a safe assumption to approximate the answer to the problem. Then we need to know the ideal gas equation and that is:
 
PV=nRT 
where 
P- pressure
V- volume
n-number of moles-
R- ideal gas constant 
T-temperature. 

Since we know that P, T and V are constant, rearranging the equation would lead to:

P/TR = n/V or the ratio of the moles of gas and volume is constant. 

(3moles)/2L = (3+x)/4L 
where 
x is the additional moles. 

Solving for x = 3 moles. 

Answer 2

Answer:

Moles of gas added = 3 moles

Explanation:

Given:

Initial volume of gas, V1 = 2.0 L

Initial moles of gas, n1 = 3 moles

Final volume, V2 = 4.0 L

To determine:

The moles of gas added to bring the final volume to 4.0 L

Explanation:

Based on the ideal gas equation

$PV = nRT$

where P = pressure, V = volume ; n = moles of gas

R = gas constant, T = temperature

At constant P and T, the above equation becomes:

V/n = constant

This is the Avogadro's law

Therefore:

$\frac{V1}{n1} = \frac{V2}{n2} \\\\n2 = \frac{V2}{V1} * n1 = \frac{4.0 L}{2.0L} * 3 = 6 moles$

The final number of moles of gas = 6

Thus, moles added = Final - Initial = n2 - n1 = 6-3 = 3 moles