Chemistry - Gas Law Stiochiometry

[sam.]

Homework Statement

Acetylene torches are used for welding. These torches use a mixture of acetylene gas, C_2H_2, and oxygen gas, O_2 to produce the following combustion reaction:

2C_2H_2(g) + 5O_2(g) --> 4CO_2(g) + 2H_2O(g)

Imagine that you have a 6.50 L gas tank and a 4.50 L gas tank. You need to fill one tank with oxygen and the other with acetylene to use in conjunction with your welding torch. If you fill the larger tank with oxygen to a pressure of 105 atm, to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time?

Homework Equations

Boyle's Law: P_1V_1 = P_2V_2
Charles Law: V_1/T_1 = V_1/T_1
Ideal Gas Law: PV = nRT

The Attempt at a Solution

Okay, I think that I have to find temperature because then I would be able to sub that into PV = nRT to find the number of moles for oxygen and then using mole ratio I can find the moles of acetylene and then sub that into the ideal gas law to find the pressure for acetylene. But I'm not exactly sure how to calculate temperature. Any help is greatly appreciated!

 

[chemisttree]

Assume room temperature.

 

[Blueshift5]

Hello! Your approach is on the right track. To find the temperature, you can use the combined gas law: P_1V_1/T_1 = P_2V_2/T_2. Since the tanks are being filled with the same amount of gas, you can set the initial pressure and volume for both tanks to be equal (105 atm and 6.50 L for oxygen, and unknown pressure and 4.50 L for acetylene). Then, solve for the unknown temperature.

Once you have the temperature, you can use the ideal gas law to find the number of moles of oxygen in the larger tank. Then, use the mole ratio from the balanced equation (5 moles of oxygen per 2 moles of acetylene) to find the number of moles of acetylene needed. Finally, use the ideal gas law again with the volume of the smaller tank and the calculated number of moles of acetylene to find the pressure needed to fill the acetylene tank.

I hope this helps! Let me know if you have any further questions.