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Chapter 11: Problem 28

A tank of acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) contains \(48.5 \mathrm{lb}\) of the gas and is at a pressure of \(600.2 \mathrm{lb} / \mathrm{in} .^{2}\) Express the pressure of the gas in atmospheres and the amount of gas in moles. \([760.0 \mathrm{~mm} \mathrm{Hg}=\) \(\left.14.696 \mathrm{lb} / \mathrm{in} .^{2}, 453.6 \mathrm{~g}=1 \mathrm{lb}\right]\)

Short Answer

Expert verified
The pressure of the acetylene gas is approximately \(30.93 \, \mathrm{mm \, Hg}\), and there are about \(846.14 \, \mathrm{mol}\) of the gas in the tank.

Step by step solution

01

Convert pressure to atmospheres

To convert the pressure of the gas from lb/in^2 to atmospheres (atm), we'll use the conversion factor given in the problem: 760.0 mm Hg = 14.696 lb/in^2. To do this, we'll set up a proportion like this: \[ \frac{600.2 \, \mathrm{lb/in^{2}}}{14.696 \, \mathrm{lb/in^{2}}} = \frac{x}{760.0 \, \mathrm{mm \, Hg}} \] Now, solve for x: \[ x = \frac{600.2 \, \mathrm{lb/in^{2}} \cdot 760.0 \, \mathrm{mm \, Hg}}{14.696 \, \mathrm{lb/in^{2}}} \] Calculating x, we get: \[ x ≈ 30.93 \, \mathrm{mm \, Hg} \] So, the pressure in atmospheres is approximately \(30.93 \, \mathrm{mm \, Hg}\).
02

Convert gas amount to moles

Now, we need to convert the amount of gas from pounds to moles. First, we'll convert from pounds to grams using the conversion rate 453.6 g = 1 lb: \[ 48.5 \, \mathrm{lb} \cdot \frac{453.6 \, \mathrm{g}}{1 \, \mathrm{lb}} = 21999.6 \, \mathrm{g} \] Next, we'll convert from grams to moles using the molecular weight of C2H2 (approximately 26 g/mol): \[ 21999.6 \, \mathrm{g} \cdot \frac{1 \, \mathrm{mol}}{26 \, \mathrm{g}} ≈ 846.14 \, \mathrm{mol} \] So, there are approximately \(846.14 \, \mathrm{mol}\) of acetylene gas in the tank.

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Most popular questions from this chapter

Which variable is not needed to describe the behavior of an ideal gas: volume, number of moles, temperature, molar mass, or pressure?

If we continuously compress a real gas in a cylinder with a movable piston while keeping the container at a constant temperature in an ice bath: (a) What will eventually happen to the gas and why? (b) How well will the ideal gas law apply to the real gas shown when it is close to doing what you said it will do in part (a)?

The gas inside a balloon is characterized by the following measurements: pressure \(=745.5 \mathrm{~mm} \mathrm{Hg}\); volume \(=250.0 \mathrm{~mL} ;\) temperature \(=25.5^{\circ} \mathrm{C}\). What is the number of moles of gas in the balloon?

What do we mean by inverse proportionality? By direct proportionality? Give an example of each using the way the pressure of a gas depends on something else.

What assumption is made for an ideal gas, and what gives us the right to make that assumption?
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