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 136 bar , to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time? Assume ideal behaviour for all gases.

2C2H2 + 5O2 ==> 4CO2 + 2H2O

Use PV = nRT and solve for mols oxygen.
Use the coefficients in the balanced equation to convert mols O2 from your first calculation above to mols C2H2.
Then use PV = nRT to convert mols C2H2 to pressure. Post your work if you get stuck.

To solve this problem, we can use the Ideal Gas Law equation:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

First, let's find the number of moles of oxygen in the 7.00 L gas tank. We know that the pressure of oxygen is 136 bar, so we convert it to Pascal (Pa) by multiplying by 100,000 (since 1 bar = 100,000 Pa):

P = 136 bar * 100,000 Pa/bar = 13,600,000 Pa

Now we can rearrange the formula to solve for the number of moles (n) of oxygen:

n = PV / RT

The ideal gas constant R is approximately 8.314 J/(mol·K), and the temperature should be in Kelvin (K). Assume room temperature is 298 K.

n = (13,600,000 Pa) * (7.00 L) / (8.314 J/(mol·K) * 298 K)

Calculating this, we find that the number of moles of oxygen is approximately 3,937.28 mol.

Next, we need to find the number of moles of acetylene. Since we want to run out of each gas at the same time, the number of moles of acetylene should be equal to the number of moles of oxygen.

Now, let's find the pressure of acetylene by rearranging the formula:

P = nRT / V

Since we already know the number of moles (n) is 3,937.28 mol, the volume V is 4.50 L, and the temperature T is 298 K, we can substitute these values into the equation:

P = (3,937.28 mol) * (8.314 J/(mol·K)) * (298 K) / (4.50 L)

Calculating this, we find that the pressure of acetylene should be approximately 173.39 bar or 17,339 KPa to run out at the same time as oxygen.