Question

A flexible container at an initial volume of 8.15 L contains 8.51 mol of gas. More gas is then added to the container until it reaches a final volume of 16.1 L . Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.

Answer 1

When the volume change to 16.1 L; the number of moles increases to 16.8 moles. This means we add 8.29 moles.

Step-by-step explanation:

Step 1: Data given

The initial volume of the container = 8.15 L

Number of moles of gas= 8.51 moles

The volume increases to 16.1 L

The pressure and temperature of the gas remain constant

Step 2: Calculate the new number of moles

V1/n1 = V2/n2

⇒with V1 = the initial volume in the container = 8.15 L

⇒with n1 = the initial number of gas = 8.51 moles

⇒with V2 = the increased volume = 16.1 L

⇒with n2 = the new number of moles = TO BE DETERMINED

8.15 L / 8.51 moles = 16.1 L / n2

n2 = 16.1 L / (8.15 L / 8.51 moles)

n2 = 16.8 moles

When the volume change to 16.1 L; the number of moles increases to 16.8 moles

The number of moles added = 16.8 - 8.51 = 8.29 moles

Answer 2

8.3 moles

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes:

Initial volume (V1) = 8.15 L

Initial mole (n1) = 8.51 mol

Final volume (V2) = 16.1 L

Number of mole added =?

Final mole (n2) =?

Step 2:

Obtaining an equation to solve for the final mole. This is illustrated below:

From ideal gas equation,

PV = nRT

Divide both side by P

V = nRT/P

Divide both side by n

V/n = RT/P

Since pressure (P) and temperature (T) are constant, therefore

V/n = constant

V1/n1 = V2/n2

Step 3:

Determination of the final mole. This is illustrated below:

Initial volume (V1) = 8.15 L

Initial mole (n1) = 8.51 mol

Final volume (V2) = 16.1 L

Final mole (n2) =?

V1/n1 = V2/n2

8.15/8.51 = 16.1/n2

Cross multiply to express in linear form

8.15 x n2 = 8.51 x 16.1

Divide both side by 8.15

n2 = (8.51 x 16.1) / 8.15

n2 = 16.81 moles

Therefore, the final mole is 16.81 moles

Step 4:

Determination of the number of moles added. This can be obtained as illustrated below:

Number of mole added = final mole - initial mole

Number of mole added = n2 - n1

Number of mole added = 16.8 - 8.51

Number of mole added = 8.3 moles