Solving Gas Law Problems: Partial Pressure & Relative Diffusion Rates

[maximade]

heres a partial pressure one:
1. A mixture of gases containing equal weights of carbon dioxide, CO, and ammonia exerts an overall pressure of 450 torr. What pressure is exerted by each gas individually?

my last question is:
2. The relative rate of diffusion between two gases is 1.89. If the lighter gas is methane (mw=16), what is the molecular weight of the other gases?

for the first one, I could probably guess and check to get my answer, but i wouldn't understand it overall. For the second one, my teacher didn't even go over rates and that stuff. Mind explaining to me how to get the answer? thank you.

 

[Borek]

1. Convert weights to moles. Partiall pressures are proportional to molar fractions.

2. Graham's law

Please note, that you should use homework template, when asking homework questions.

 

[Blueshift5]

1. To solve this problem, we can use the ideal gas law, which states that the pressure (P) of a gas is equal to its number of moles (n) multiplied by its molar gas constant (R) and its temperature (T). We can rearrange this equation to solve for the number of moles of each gas: n = P/RT.

Since the weights of carbon dioxide (CO2) and ammonia (NH3) are equal, we can assume that they have the same number of moles. Therefore, we can set up the following equation:

(450 torr) / (R * T) = (nCO2 + nNH3)

To solve for the pressure exerted by each gas individually, we need to find the number of moles of each gas. We can do this by setting up a system of equations, using the molecular weights of each gas.

Let's call the molecular weight of CO2 "x" and the molecular weight of NH3 "y."

x * nCO2 = y * nNH3

x = 44 g/mol (molecular weight of CO2)

y = 17 g/mol (molecular weight of NH3)

Substituting these values into our first equation, we get:

(450 torr) / (R * T) = (44 * nCO2 + 17 * nNH3)

Now, we also know that the number of moles of each gas is the same, so we can set nCO2 equal to nNH3:

(450 torr) / (R * T) = (44 * nCO2 + 17 * nCO2)

(450 torr) / (R * T) = (61 * nCO2)

nCO2 = (450 torr) / (61 * R * T)

Now, we can plug this value into our original equation to solve for the pressure exerted by each gas:

P(CO2) = (450 torr) / (61 * R * T) * 44 = 29.5 torr

P(NH3) = (450 torr) / (61 * R * T) * 17 = 11.5 torr

Therefore, the individual pressures exerted by carbon dioxide and ammonia are 29.5 torr and 11.5