A flexible container at an initial volume of 4.11 L contains 2.51 mol of gas. More gas is then added to the container until it reaches a final volume of 16.9 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.

7.81 moles

Explanation:

To solve this problem, let us generate an expression involving volume and number of mole of the gas since the pressure and temperature of the gas are constant.

From ideal gas equation:

PV = nRT

Divide both side by P

V = nRT/P

Divide both side by n

V/n = RT/P

Since RT/P are constant, then:

V1/n1 = V2/n2

Data obtained from the question include:

V1 = 4.11

n1 = 2.51 moles

V2 = 16.9L

n2 = ?

Using the above equation i. e V1/n1 = V2/n2, the final number of the gas can be obtained as illustrated below:

4.11/2.51 = 16.9/n2

Cross multiply to express in linear form

4.11 x n2 = 2.51 x 16.9

Divide both side by 4.11

n2 = (2.51 x 16.9) / 4.11

n2 = 10.32moles

Now, to obtain the number of mole of the gas added, we'll subtract the initial mole from the final mole i. e

n2 - n1

Number of mole added = n2 - n1

10.32 - 2.51 = 7.81 moles

Therefore, 7.81 moles of the gas was added to the container