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

Moles of gas added = 3 moles

Step-by-step 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

Step-by-step 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:

`(V1)/(n1) = (V2)/(n2) \\\\n2 = (V2)/(V1) * n1 = (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