A flexible container at an initial volume of 4.11 L contains 7.51 mol of gas. More gas is then added to the container until it reaches a final volume of 15.9 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
at constant temp and pressure, the volume is directly related to the number of moles
added moles = new moles - 7.51 mol = 7.51 [(15.9 / 4.11) - 1]
To solve this problem, we will use the ideal gas law, which states:
PV = nRT
Where:
P = pressure of the gas (constant)
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas (constant)
Since the pressure and temperature remain 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
Let's substitute the given values:
V1 = 4.11 L
n1 = 7.51 mol
V2 = 15.9 L
Now, let's solve for n2:
V1 / n1 = V2 / n2
4.11 L / 7.51 mol = 15.9 L / n2
Cross-multiplying:
4.11 L * n2 = 7.51 mol * 15.9 L
Simplifying:
n2 = (7.51 mol * 15.9 L) / 4.11 L
n2 = 1167.09 mol
Therefore, the number of moles of gas added to the container is approximately 1167.09 mol.
To calculate the number of moles of gas added to the container, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant)
V = volume
n = number of moles
R = ideal gas constant
T = temperature (constant)
Because the pressure and temperature of the gas remain constant, we can simplify the equation to:
V1 / n1 = V2 / n2
Where:
V1 = initial volume
n1 = initial number of moles
V2 = final volume
n2 = final number of moles
Let's plug in the given values into the equation:
V1 = 4.11 L
n1 = 7.51 mol
V2 = 15.9 L
n2 = ? (number of moles to be calculated)
4.11 / 7.51 = 15.9 / n2
Now, let's solve for n2 by cross-multiplying:
4.11 * n2 = 7.51 * 15.9
n2 = (7.51 * 15.9) / 4.11
n2 = 29.086 mol
Therefore, the number of moles of gas added to the container is approximately 29.086 mol.