magine that you have a 7.00 L gas tank and a 3.50 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? Assume ideal behavior for all gases.

Question

magine that you have a 7.00 L gas tank and a 3.50 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? Assume ideal behavior for all gases.

Answer 1

1. Write the equation and balance it.

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

2. How many moles O2 do you have? pV = nRT. Solve for n.
3. Using the coefficients in the balanced equation, convert moles O2 to moles C2H2.
4. Now convert moles C2H2 to p using PV = nRT.

Answer 2

To determine the pressure at which you should fill the acetylene tank, you can use the concept of the ideal gas law and the principle of equal moles.

Step 1: Find the volume of each gas using the ideal gas law.
The ideal gas law is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

For both gases, we can assume the temperature and moles are constant. Thus, we can rewrite the equation as:
(P1 * V1) / (P2 * V2) = (n1 * R * T) / (n2 * R * T)

By canceling out the constant terms, we obtain:
(P1 * V1) / (P2 * V2) = n1 / n2

Step 2: Relate the volumes of the two tanks.
We are given that the larger tank has a volume of 7.00 L (V1) and the smaller tank has a volume of 3.50 L (V2).

Step 3: Determine the moles of each gas.
Since we want both gases to run out at the same time, the two tanks must contain the same number of moles.

Let's assume that the moles of oxygen (n1) and acetylene (n2) are equal and represented by the variable "x."

Step 4: Calculate the pressure of each gas.
Using the information from steps 2 and 3, we can rewrite the equation as:
(105 atm * 7.00 L) / (P2 * 3.50 L) = x / x

Simplifying this equation, we get:
2 = P2 / 105

Solving for P2, we find:
P2 = 105 * 2
P2 = 210 atm

So, you should fill the acetylene tank to a pressure of 210 atm to ensure that you run out of each gas at the same time.