a flexible container at an initial volume of 7.14L contains 9.51mol of gas. more gas is then added to the container until it reaches final volume of 17.1L. assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
To calculate the number of moles of gas added to the container, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure of the gas (which is assumed to remain constant)
V = volume of the gas
n = number of moles of gas
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature of the gas (which is assumed to remain constant)
We are given:
Initial volume (V1) = 7.14 L
Number of moles (n1) = 9.51 mol
Final volume (V2) = 17.1 L
Since the pressure and temperature remain constant, we can set up the following equation using the ideal gas law:
(P1 * V1) = n1 * R * T1
(P2 * V2) = (n1 + x) * R * T2
where x represents the number of moles of gas added, and P1, P2, T1, and T2 are the initial and final pressure and temperature, respectively.
Since the pressure and temperature remain constant, we can simplify the equation:
(V1 / V2) = n1 / (n1 + x)
Now let's solve for x:
(V2 / V1) = (n1 + x) / n1
(V2 / V1) * n1 = n1 + x
(V2 / V1) * n1 - n1 = x
(V2 / V1 - 1) * n1 = x
Now we can plug in the given values:
V1 = 7.14 L
n1 = 9.51 mol
V2 = 17.1 L
Calculating:
x = (17.1 / 7.14 - 1) * 9.51
x = 10.1 * 9.51
x = 95.99
Therefore, the number of moles of gas added to the container is approximately 96 moles.