A 1.00-L bulb contains a sample of O2 at 25°C and 1.00 atm pressure. A second 1.00-L bulb contains a sample of CH4 at 25°C and 1.00 atm pressure. What is the ratio of the number of molecules of methane to the number of molecules of oxygen in each of the containers?
A) 1:1
B) 5:2
C) 2:5
D) square root of 32:16
E) square root of 16:32
A) 1:1
B) 5:2
C) 2:5
D) square root of 32:16
E) square root of 16:32
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Use the ideal pressure equation to calculate the number of moles (n) of each:
PV = nRT ==> n = PV/RT
where: P = Pressure in atmospheres, V = Volume in liters, T = Absolute temperature in Kelvins, R = 0.0821
n(O2) = (1.00 atm)(1.00 L) / (0.0821)(298 K) = 0.0402 mol O2
n(CH4) = (1.00 atm)(1.00 L) / (0.0821)(298 K) = 0.0402 mol CH4
There are 6.02 x 10²³ molecules in one mole of any substance. Since there are equal numbers of moles of oxygen and methane, there are equal numbers of molecules of each gas.
The answer is A
A really easy way of solving this is to notice that the only difference between the two gases, is the gases themselves. Both gases occupy equal volumes at equal temperature and pressure. Therefore each has the same number of moles, hence the same number of molecules, as the other.
PV = nRT ==> n = PV/RT
where: P = Pressure in atmospheres, V = Volume in liters, T = Absolute temperature in Kelvins, R = 0.0821
n(O2) = (1.00 atm)(1.00 L) / (0.0821)(298 K) = 0.0402 mol O2
n(CH4) = (1.00 atm)(1.00 L) / (0.0821)(298 K) = 0.0402 mol CH4
There are 6.02 x 10²³ molecules in one mole of any substance. Since there are equal numbers of moles of oxygen and methane, there are equal numbers of molecules of each gas.
The answer is A
A really easy way of solving this is to notice that the only difference between the two gases, is the gases themselves. Both gases occupy equal volumes at equal temperature and pressure. Therefore each has the same number of moles, hence the same number of molecules, as the other.