chem question for chem weez

[Smooth Operater]

2X + Y --> Z

IF stoichiometric quantities of X and Y are placed in a sealed, flexiable container container with an initial volume of 30 L at STP, what volume of Z will be produced? Given that XYZ are gases.

The correct answer is 10 L. But I don't understand the logic behind getting the answer. If someone can explain it, it will be great. thanks as always!

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[djeffreyt]

It's a bit of a tricky question since we're so used to dealing with reactions that don't go all the way to completion, but that is what is being assumed here.

basically we put 2 moles of X and 1 mole of Y into a container of 30L at STP and we assume the reaction goes to completion. Volume of a gas is dependent only on moles of gas particles present, so initially we put in 3 moles of a gas and they react to completion to form 1 mole of Z.

so if
V' = initial volume
n' = initial moles of gas
V" = final volume
n" = final moles of gas

then

V'/n' = V"/n"

30 L / 3 moles = V" / 1 mole

V" = 10 L

 

[714guy]

2X + Y --> Z

IF stoichiometric quantities of X and Y are placed in a sealed, flexiable container container with an initial volume of 30 L at STP, what volume of Z will be produced? Given that XYZ are gases.

The correct answer is 10 L. But I don't understand the logic behind getting the answer. If someone can explain it, it will be great. thanks as always!

my logic . . . since we know that at STP 1 mole of gas occupies 22.414L, making 1/2 mole of gas @ STP occupying 1/2 of 22.414L. But in this case we have a total of 30L of stoichiometric quantities of X and Y, so that would mean twice as much X than Y in the 30L. so X = 20L and Y= 10L using stoichi, we can find that we'll make 10L of Z.

Please correct me if I am wrong about this. Thanks

 

[allstardentist]

Initially, the volume is 30L at STP. This means that there are a total of 30/22.4 moles of reactants. Since we know that X and Y are in 2:1 ratio, the mole fraction of Y will be 1/(2+1). So we have (30/22.4 x 1/3) moles of Y.Also, 1 mole of Y yields 1 mole of Z, thus, # of moles of Z = (30/22.4 x 1/3). Lastly, we calculate the volume by multiplying the number of moles of Z by 22.4 L/1mole. This is the most simplified explanation I can think of. Hope it helps.