A 12.3 vessel was found to contain N2, Ar He, and He. The total pressure in the vessel was 987 torr and the partial pressures of nitrogen, argon, and helium were 44 torr, 486 torr, and 218 torr, respectively. What was the pressure of neon in the vessel?
sum of partial pressures= total pressure
To find the pressure of neon in the vessel, we first need to determine the moles of each gas present using the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
First, let's find the moles of nitrogen (N2):
n(N2) = (P(N2) * V) / (R * T)
Given:
P(N2) = 44 torr
V = 12.3 L
R (ideal gas constant) = 0.0821 L·atm/(mol·K) or 62.36 torr·L/(mol·K) (torr is used for consistency)
T (temperature) is not provided, so we assume it is constant.
Now, let's find the moles of argon (Ar):
n(Ar) = (P(Ar) * V) / (R * T)
Given:
P(Ar) = 486 torr
V = 12.3 L
R = 62.36 torr·L/(mol·K) (the same constant as before)
Finally, let's find the moles of helium (He):
n(He) = (P(He) * V) / (R * T)
Given:
P(He) = 218 torr
V = 12.3 L
R = 62.36 torr·L/(mol·K) (the same constant as before)
Now, we know that the total pressure is the sum of the partial pressures of all the gases:
P(total) = P(N2) + P(Ar) + P(He) + P(Ne)
Given:
P(total) = 987 torr
Since neon (Ne) is the only gas left, we can find its pressure by subtracting the sum of the partial pressures of N2, Ar, and He from the total pressure:
P(Ne) = P(total) - (P(N2) + P(Ar) + P(He))
Now, let's plug in the previously calculated values:
P(Ne) = 987 torr - (44 torr + 486 torr + 218 torr)
P(Ne) = 239 torr
Therefore, the pressure of neon in the vessel is 239 torr.