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Chapter 11: Problem 49

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?

Short Answer

Expert verified
The number of moles of gas inside the balloon is approximately 0.01001 mol.

Step by step solution

01

Convert given values to appropriate units

First, we need to convert the given pressure, volume, and temperature into their appropriate units: SI units for pressure (atmosphere) and temperature (Kelvin). Pressure: \(745.5 \mathrm{~mm} \mathrm{Hg}\) is equal to \(745.5 \times \frac{1 \mathrm{~atm}}{760 \mathrm{~mm} \mathrm{Hg}} = 0.9809 \mathrm{~atm}\) Volume: \(250.0 \mathrm{~mL}\) is equal to \(250.0 \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}} = 0.2500 \mathrm{~L}\) Temperature: \(25.5^{\circ} \mathrm{C}\) is equal to \(25.5 + 273.15 = 298.65 \mathrm{~K}\)
02

Apply the Ideal Gas Law

Now we can apply the Ideal Gas Law with our converted values: PV = nRT R (Ideal Gas Constant) = \(0.0821 \frac{\mathrm{L \cdot atm}}{\mathrm{mol \cdot K}}\) Our equation now becomes: \((0.9809 \mathrm{~atm})(0.2500 \mathrm{~L}) = n (0.0821 \frac{\mathrm{L \cdot atm}}{\mathrm{mol \cdot K}})(298.65 \mathrm{~K})\)
03

Solve for the number of moles, n

Now, we can solve the equation for the number of moles, n: \(n = \frac{(0.9809 \mathrm{~atm})(0.2500 \mathrm{~L})}{(0.0821 \frac{\mathrm{L \cdot atm}}{\mathrm{mol \cdot K}})(298.65 \mathrm{~K})}\) \(n = \frac{0.2452 \mathrm{~atm \cdot L}}{24.5093 \frac{\mathrm{atm \cdot L}}{\mathrm{mol}}}\) \(n = 0.01001 \mathrm{~mol}\) So, the number of moles of gas inside the balloon is approximately 0.01001 mol.

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Most popular questions from this chapter

A chemistry student realizes she has forgotten the value of \(R\) and needs to determine it experimentally. She decides to measure the mass, volume, pressure, and temperature of a sample of carbon dioxide gas. She finds that \(4.505 \mathrm{~g}\) of the gas occupies \(2.50 \mathrm{~L}\) at \(23^{\circ} \mathrm{C}\) and \(0.9960 \mathrm{~atm}\). Calculate the value of \(R\) she determines from these data.

Why are the results that are calculated using the ideal gas law not exactly equal to the "true" results obtained by an experimental measurement?

Consider a container that contains \(1.00\) mole of \(\mathrm{CO}_{2}(g)\) at \(298 \mathrm{~K}\). (a) What does the ideal gas law predict the pressure to be in atm? (b) What does the van der Waals equation predict the pressure to be? (c) What is the percent difference of the van der Waals pressure from the ideal pressure? (d) Suppose you increased the temperature to \(1000 \mathrm{~K}\). Would you expect the percent difference to increase or decrease compared to your answer in (c)? Explain.

What is the Celsius temperature of a gas if \(3.200\) moles of it occupy \(12.00 \mathrm{~L}\) at \(8.500 \mathrm{~atm} ?\)

You are on the balcony of the upper floor of a high-rise building in Chicago. Way down below on the street, your friend is engaged in conversation with someone and is drinking a particularly flavorful mixed drink. You decide to take a sip from his glass without his knowing, so you collect together every drinking straw in the apartment and start taping them together to create a very long drinking straw. If the atmospheric pressure is currently \(760 \mathrm{~mm} \mathrm{Hg}\), what is the longest straw you can use to get a sip of your friend's drink? (Assume the density of the drink is the same as pure water, \(1.0 \mathrm{~g} / \mathrm{mL}\).)
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