Question

Acetylene torches are used for welding. These torches use a mixture of acetylene gas, C2H2C2H2, and oxygen gas, O2O2 to produce the following combustion reaction:

2C2H2(g)+5O2(g)→4CO2(g)+2H2O(g)

Imagine that you have a 7.00 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 115 atm , to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time? Assume ideal behavior for all gases.

Answer 1

The given combustion reaction of acetylene gas is

2C₂H_2(g) + 5O_2(g) → 4CO_2(g) + 2H₂O_(g)  

i.e for complete combustion, 2 moles of C₂H_2(g) require 5 moles of O_2(g) and produce 4 moles of CO_2(g) and 2 moles of H₂O_(g) as product

Now given

The larger tank with volume (V) = 7.00 L contains oxygen

Now the pressure (P) of the gas = 115 atm

So if we consider the temp to be constant (lets take it as 1 K), then the mols of oxygen gas present is calculated by using Ideal gas equation-

PV = nRT

where

n = moles of gas present

R = gas constant = 0.0821 L.atm/mol.K

Now putting the values-

PV = nRT

115 atm * 7.00 L = n (0.0821 L.atm/mol.K) * 1 K

805‬ = n (0.0821 /mol)

n = 805‬ / (0.0821 /mol)

= 9,805 mols

That means in the larger tank, mols of Oxygen present = 9,805 mols

Now from the equation, we can see

5 moles of O_2(g) require 2 moles of C₂H_2(g) for complete combustion

So 9,805 moles of O_2(g) require = 2/5 * 9,805

= 3,922 moles of C₂H_2(g) for complete combustion

That means in the smaller tank, we have 3,922 moles of C₂H_2(g)

Again given volume of the smaller tank = 4.5 L

So to calculate the pressure in this smaller tank, lets put the values in the formula-

PV = nRT

P * 4.5 L = 3,922 moles * (0.0821 L.atm/mol.K) * 1 K

P‬ = 3,922 moles * (0.0821 L.atm/mol.K) / 4.5 L

P = 71.55 atm

That means we need to fill the tank of Acetylene with pressure of 71.55 atm. So that due to actetylene having at a lesser pressure and Oxygen having a higher pressure, Oxygen will start moving toward the acetylene tank and reaction starts