If there are 2L of H2 gas at .625 atm, and 1L of N2 gas at .200 atm isolated in two flasks, what are the final partial pressures of each, and the total pressure, after the valve between the two flasks has been opened and the gases are allowed to mix? Is this simply a ratio problem? If I don't have the masses of each, what do I do?
you
To determine the final partial pressures of each gas and the total pressure after mixing, we can use Dalton's law of partial pressures.
Dalton's law states that the total pressure exerted by a mixture of gases is equal to the sum of the pressures that each gas would exert if it were alone in the container. In equation form, it looks like this:
P_total = P_1 + P_2 + ...
Where P_total is the total pressure, and P_1, P_2, etc. are the partial pressures of each gas.
In this case, we have 2L of H2 gas at 0.625 atm and 1L of N2 gas at 0.200 atm. To find the final partial pressures and the total pressure, we need to consider the number of moles of each gas.
Since we don't have the masses of each gas, we can use the ideal gas law equation, which relates pressure, volume, temperature, and the number of moles of a gas. The ideal gas law is expressed as:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
We can rearrange this equation to solve for the number of moles:
n = PV / RT
Now, let's apply this equation to each gas:
For the H2 gas:
n_H2 = (0.625 atm) * (2 L) / (R * T)
For the N2 gas:
n_N2 = (0.200 atm) * (1 L) / (R * T)
Since the temperature and the gas constant are constant, the ratio of the number of moles of H2 to N2 will be the same as the ratio of their partial pressures.
Now, to calculate the partial pressures, we need to find the total number of moles of gas. We can add the number of moles of H2 and N2:
n_total = n_H2 + n_N2
The final partial pressure of each gas can be calculated using the following ratios:
P_H2 = (n_H2 / n_total) * P_total
P_N2 = (n_N2 / n_total) * P_total
Finally, the total pressure P_total will be the sum of the partial pressures:
P_total = P_H2 + P_N2
By following these steps, we can determine the final partial pressures of each gas and the total pressure after the gases have mixed. It is not simply a ratio problem, as we need to consider the number of moles of each gas using the ideal gas law.