A tank contains a mixture of 3.0 mol of nitrogen 2.0 mol of oxygen and 1 mol of carbon dioxide at 25 degrees and a total pressure of 10 ATM calculate the partial pressure in torr of each gas?
XN2 = moles N2/total moles.
XCO2 = same thing
XO2 = same
pN2 = XN2*Ptotal
pCO2 = XCO2*Ptotal
pO2 = XO2*Ptotal
To calculate the partial pressure of each gas in torr, we need to apply Dalton's law of partial pressures. According to Dalton's law, the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of each gas.
First, we convert the total pressure from ATM to torr. Since 1 ATM is equal to 760 torr, we multiply the total pressure by 760 to convert it:
Total pressure in torr = 10 ATM * 760 torr/1 ATM = 7600 torr
Next, we calculate the partial pressure of each gas. The partial pressure of a gas can be calculated using its mole fraction.
The mole fraction of a gas is calculated by dividing the moles of the gas by the total moles of all gases in the mixture.
Mole fraction of nitrogen = moles of nitrogen / total moles
Mole fraction of oxygen = moles of oxygen / total moles
Mole fraction of carbon dioxide = moles of carbon dioxide / total moles
Given:
moles of nitrogen = 3.0 mol
moles of oxygen = 2.0 mol
moles of carbon dioxide = 1.0 mol
total moles = 3.0 mol + 2.0 mol + 1.0 mol = 6.0 mol
Mole fraction of nitrogen = 3.0 mol / 6.0 mol = 0.5
Mole fraction of oxygen = 2.0 mol / 6.0 mol = 0.3333 (rounded to four decimal places)
Mole fraction of carbon dioxide = 1.0 mol / 6.0 mol = 0.1667 (rounded to four decimal places)
Finally, we calculate the partial pressure of each gas by multiplying its mole fraction by the total pressure:
Partial pressure of nitrogen = mole fraction of nitrogen * total pressure
Partial pressure of oxygen = mole fraction of oxygen * total pressure
Partial pressure of carbon dioxide = mole fraction of carbon dioxide * total pressure
Partial pressure of nitrogen = 0.5 * 7600 torr = 3800 torr
Partial pressure of oxygen = 0.3333 * 7600 torr = 2539.8 torr (rounded to two decimal places)
Partial pressure of carbon dioxide = 0.1667 * 7600 torr = 1267.2 torr (rounded to two decimal places)
Therefore, the partial pressure in torr of each gas are as follows:
Nitrogen: 3800 torr
Oxygen: 2539.8 torr
Carbon dioxide: 1267.2 torr