How do I solve this Chemistry gas problem?

Question

I have tried about a million ways to figure this problem and just don't know how. My professor told us to teach ourselves from the book but the book does not cover this type of problem or it is going over my head. Please explain how to solve it. Don't just give an answer I need to know how to do it for a test.



Nitroglycerin (227.1 g/mole) decomposes according to the reaction below.


4 C3H5N3O9(Liquid) yields 6 N2(gas) + 12 CO2(gas) + 10 H20(g) +O2(gas)

What total volume of gases is produced at 65 degrees C and 744 mm Hg by the decomposition of 5.00g nitroglycerin? (R=0.08206 L atm/mol k)

On a website I found it says the answer is 4.52 L but I don't not know how they found that answer.

Answer 1

Mols of nitroglycerin= 5/227.1 = 0.02202 mol

From the reaction:
1 mol nitroglycerin ≡ 1.5 mol N2 ≡ 3 mol CO2 ≡ 2.5 mol H2O ≡ 0.25 mol O2

Molar volume occupied by any gas at STP by avagadros law = 22.414 L

STP conditions are:
P = 1 atm = 760 mm of Hg
T = 273.15 K

At STP:

0.02202 mol nitroglycerin ≡ 0.03303 mol N2 ≡ 0.06606 mol CO2 ≡ 0.05505 mol H2O ≡ 0.005505 mol O2

From Ideal gas equation :

P1*V1/T1 = P2*V2/T2

Since P and T for all gases are same:

V2 = P1*T2*V1/(P2*T1)

V1 = 22.414 (0.03303 + 0.06606 + 0.05505 + 0.005505 )
= 22.414 *0.159645
= 3.57828303 L

V2 = 760*(273.15 + 65)*3.57828303/(744*273.15) = 4.5251 L

Answer 2

This problem is one of the ideal gas problems. Since the problem gave you the temperature T (65 degrees C), the pressure P (744 mmHg) and the constant value R (0.08206 L atm/mol K) so you can think about the ideal gas equation: P*V = n*R*T. From this equation, you can get: V = (n*R*T)/P.
From this equation, you know the 3 variables (R, T, and P) so the only thing you need to find is n which is the mole of the product.
According to the reaction above, the total moles of the products are equal to total moles of the reactant. There is only one reactant in this reaction which is C3H5N3O9. In order to find the moles of C3H5N3O9, use the equation: n = m/M where m is the total amount of nitroglycerin that was used (5.00g) and M is the molar mass of nitroglycerin (227.1 g/mol).
So now you have the mole n, just plug it back in the first equation V= (n*R*T)/P you can find the total volume of gases is produced.
Notes: In this equation, T is used as Kelvin degree, not Celcius. To get T in Kelvin: T(K) = T(C) + 273.15
Good luck!
P/S: the result you found from that website is wrong, 4 L of gas is alot!!!!! If you notice you only used 5g of starting material, how can you end up getting 4L of gas?!

Answer 3

You would have to use the formula pV = nRT

mol of nitroglycerin = 5/(3*12 + 5 + 14*3 + 16*9) = 8.81E-3 mol
mol of gas produced = (8.81E-3/4)(6+12+10+1) = 0.0639 mol
pressure = 744/760 = 0.979 atm
0.979V = 0.0639(0.08206)(338)
V = 1.81 L

Not too sure whether 744mmHg = 1atm. If it is, the volume will then be 1.77L.

Answer 4

the quantity of a gasoline relies upon on the temperature and the strain using fact the strain drops the quantity will boost. Temperature right this isn't changing, so we are able to apply: P1V1 = P2V2 for this reason: V1 x (P1/P2) = V2; 2.50L x (a million.15/a million.00) = 2.875L