Final answer:
To find the mole fraction of each gas in the mixture, use the ideal gas law to calculate the number of moles of each gas, then divide by the total number of moles. To calculate the total number of moles of gas in the mixture, use the ideal gas law with the total pressure and volume. To calculate the number of grams of each gas, convert the number of moles to grams using the molar mass.
Step-by-step explanation:
a. To find the mole fraction of each gas in the mixture, we need to first find the total number of moles of gas in the mixture. This can be done using the ideal gas law:
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.
From the problem, we are given the partial pressures of CH₄(g) and O₂(g) and the volume of the mixture. Assuming the temperature is constant, we can use the ideal gas law to find the number of moles of each gas:
n(CH₄) = (P(CH₄) * V) / (R * T)
n(O₂) = (P(O₂) * V) / (R * T)
Then, we can calculate the total number of moles of gas in the mixture by adding the number of moles of CH₄ and O₂:
n(total) = n(CH₄) + n(O₂)
Finally, we can find the mole fraction of each gas by dividing the number of moles of each gas by the total number of moles:
X(CH₄) = n(CH₄) / n(total)
X(O₂) = n(O₂) / n(total)
b. To calculate the total number of moles of gas in the mixture, we can use the ideal gas law as described in part a:
n(total) = (P(total) * V) / (R * T)
c. To calculate the number of grams of each gas in the mixture, we need to convert the number of moles to grams. The molar mass of each gas can be found in the periodic table or a chemistry reference book. The number of grams can be calculated using the equation:
mass = n * molar mass