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Chapter 11: Problem 88

Carbon dioxide in a gas cylinder of unchangeable volume is at a pressure of \(25.0 \mathrm{~atm}\) at \(25^{\circ} \mathrm{C}\). When placed in the sunlight on a hot summer day, the temperature increases to \(40^{\circ} \mathrm{C}\). What is the new pressure of the \(\mathrm{CO}_{2}\) ?

Short Answer

Expert verified
The new pressure of the \(\mathrm{CO}_{2}\) gas when the temperature increases to \(40^{\circ} \mathrm{C}\) is \(26.3 \mathrm{~atm}\).

Step by step solution

01

Write down the Gay-Lussac's Law equation

The equation for Gay-Lussac's Law is given as: \(P_1/T_1 = P_2/T_2\) Here, \(P_1\) is the initial pressure, \(T_1\) is the initial temperature, \(P_2\) is the final pressure and \(T_2\) is the final temperature.
02

Convert the temperatures to Kelvin

As we know, to work with gas laws, we need to have temperatures in Kelvin. Let's convert the given temperatures from Celsius to Kelvin: Initial temperature (\(T_1\)): \(25^{\circ} \mathrm{C} + 273.15 = 298.15 \mathrm{K}\) Final temperature (\(T_2\)): \(40^{\circ} \mathrm{C} + 273.15 = 313.15 \mathrm{K}\)
03

Substitute the given values into the equation

Now, we will substitute the given values into the Gay-Lussac's Law equation: \(\frac{25.0 \mathrm{~atm}}{298.15 \mathrm{K}} = \frac{P_2}{313.15 \mathrm{K}}\)
04

Solve for the final pressure (\(P_2\))

To find the new pressure of the \(\mathrm{CO}_{2}\) gas, rearrange and solve for \(P_2\): \(P_2 = \frac{25.0 \mathrm{~atm} \times 313.15 \mathrm{K}}{298.15 \mathrm{K}}\) Now, calculate the new pressure: \(P_2 = 26.3 \mathrm{~atm}\)
05

State the answer

The new pressure of the \(\mathrm{CO}_{2}\) gas when the temperature increases to \(40^{\circ} \mathrm{C}\) is \(26.3 \mathrm{~atm}\).

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Most popular questions from this chapter

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, \(1.0 \mathrm{~g} / \mathrm{mL}\).)

Perform the following conversions: (a) \(30.2\) in. \(\mathrm{Hg}\) to millimeters of mercury (b) \(890.0 \mathrm{~mm} \mathrm{Hg}\) to atmospheres (c) \(300.0 \mathrm{lb} / \mathrm{in} .^{2}\) to atmospheres

According to the ideal gas law, what would happen to the pressure of a gas if you doubled the amount of gas in a container while also tripling the Kelvin temperature of the gas? Explain.

Explain why gases always occupy the entire container they are in, but solids and liquids do not.

A tank of \(\mathrm{O}_{2}\) gas is stored in a cool basement \(\left(T=10.0^{\circ} \mathrm{C}\right)\). Its pressure gauge reads \(50.5 \mathrm{lb} / \mathrm{in} .^{2} .\) Diver Dan then places the tank in his truck, where the sun warms it to \(20.0^{\circ} \mathrm{C}\). What does the pressure gauge read at this elevated temperature?
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