A flexible container at an initial volume of 8.15 L contains 2.51 mol of gas. More gas is then added to the container until it reaches a final volume of 12.1 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.

The easy way to do this is to recognize that you use PV = nRT and that P, R, and T are constant; therefore we can re-write the equation as k1V = n*k2*k3 or

V = n*k2k3/k1 and since k2k3/k1 is just another constant we can re-write that as V = nk. Solve for k = V/n - 8.1/2.51 = ?

Then n = V/k = 12.1/k from above = ?. Subtract this last n - first n to find how much was added.

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas

Since the pressure and temperature are constant, we can rewrite the equation as:

V1/n1 = V2/n2

Where:
V1 = initial volume
n1 = initial number of moles
V2 = final volume
n2 = final number of moles

In this case, we are given:
V1 = 8.15 L
n1 = 2.51 mol
V2 = 12.1 L

We need to calculate n2, the final number of moles.

Rearranging the equation, we can solve for n2:

n2 = (V2 * n1) / V1

Substituting the values, we have:

n2 = (12.1 L * 2.51 mol) / 8.15 L

Calculating this expression:

n2 = (30.431 L•mol) / 8.15 L ≈ 3.741 mol

Therefore, approximately 3.741 moles of gas were added to the container to reach the final volume of 12.1 L.