How to Calculate the Partial Pressure of Propane in a Mixture?

[Daizy5936]

I am having the hardest time figuring this one out:

"Calculate the partial pressure of propane in a mixture that contains equal numbers of moles of propane (C3H8) and butane (C4H10) at 20 °C and 1918 mmHg. Give your answer in mmHg"

Can anybody help me out? I'm so lost!

 

[gravenewworld]

In general the Total P=P1+P2+P3... where P1,2,3 etc are the pressures of each substance, which can be found using the ideal gas law
P_i=n_iRT/V. RT/V can be replaced by P/n (P is total pressure remember )giving you P_i=n_iP/n=yiP, where yi is the mole fraction of the substance i.
The problem gives you total pressure and says that you have equal amounts of moles of each substance. Therefore mole fraction for each substance is= to 1/2 because you have equal amounts. So P1=.5P=959 mmHg and P2=.5P=959mmHg.

 

[ravenprp]

Calculating partial pressure involves using the ideal gas law, which states that the pressure of a gas is equal to the number of moles of the gas multiplied by the gas's molar volume and the temperature in Kelvin. In this case, we are given the temperature and total pressure of the mixture, so we can use the ideal gas law to solve for the partial pressure of propane.

First, we need to find the total number of moles in the mixture. Since we are told that the mixture contains equal numbers of moles of propane and butane, we can assume that there is an equal number of moles of each gas. Therefore, we can calculate the total number of moles by dividing the total pressure (1918 mmHg) by the molar volume at STP (22.4 L/mol):

n = P/VM = (1918 mmHg)(1 atm/760 mmHg)(22.4 L/mol) = 29.68 mol

Next, we need to find the molar fraction of propane in the mixture. This is the ratio of moles of propane to the total moles in the mixture:

Xpropane = npropane/ntotal = 1 mol/29.68 mol = 0.0337

Now, we can use the ideal gas law to solve for the partial pressure of propane:

Ppropane = Xpropane * Ptotal = (0.0337)(1918 mmHg) = 64.6 mmHg

Therefore, the partial pressure of propane in the mixture is 64.6 mmHg.