/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 67 A piece of dry ice (solid carbon... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 67

A piece of dry ice (solid carbon dioxide) with a mass of 5.50 \(\mathrm{g}\) is placed in a 10.0 -L vessel that already contains air at 705 torr and \(24^{\circ} \mathrm{C}\) . After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO\(_{2}\) gas, and the total pressure in the container at \(24^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The partial pressure of CO2 in the container after the dry ice has completely sublimed is approximately \(0.3075\:atm\) and the total pressure is approximately \(1.2351\:atm\) at \(24^{\circ}C\).

Step by step solution

01

Find moles of CO2 produced

First, we need to find the moles of solid CO2 that will sublimate to form gas. Use the mass and molar mass of CO2 (44.01 g/mol) to perform this calculation. moles of CO2 = mass of CO2 / molar mass of CO2 moles of CO2 = 5.50 g / 44.01 g/mol
02

Calculate the partial pressure of CO2

Next, we will use the ideal gas law to find the partial pressure of CO2. The ideal gas law formula is: PV = nRT Where: P = pressure V = volume n = moles of gas R = ideal gas constant (0.0821 L atm/mol K) T = temperature in Kelvin First, we need to convert the temperature from Celsius to Kelvin. T(K) = T(掳C) + 273.15 T(K) = 24 + 273.15 = 297.15 K Now we can use the ideal gas law to find the partial pressure of CO2. P(CO2) = n(CO2)RT / V P(CO2) = (moles of CO2) (0.0821 L atm/mol K) (297.15 K) / 10.0 L
03

Convert initial pressure to atmospheres

The initial pressure in the container is given in torr. We need to convert this pressure to atmospheres, since our ideal gas constant uses units of "atm." To do so, use the conversion factor: 1 atm = 760 torr Initial pressure (atm) = 705 torr / 760 torr/atm
04

Calculate the total pressure

Now we can find the total pressure in the container after the CO2 has sublimated. Simply add the partial pressure of CO2 to the initial pressure in the container. Total pressure = Initial pressure (atm) + P(CO2) Final step: fill-in calculations from previous steps moles of CO2 = 5.50 g / 44.01 g/mol = 0.125 mol P(CO2) = (0.125 mol) (0.0821 L atm/mol K) (297.15 K) / 10.0 L = 0.3075 atm Initial pressure (atm) = 705 torr / 760 torr/atm = 0.9276 atm Total pressure = 0.9276 atm + 0.3075 atm = 1.2351 atm The partial pressure of CO2 in the container after the dry ice has completely sublimed is approximately 0.3075 atm and the total pressure is approximately 1.2351 atm at 24掳C.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ideal Gas Law
Understanding ideal gas law is crucial when dealing with problems related to the behavior of gases. The ideal gas law is a fundamental equation that relates the four properties of a gas: pressure (P), volume (V), number of moles (n), and temperature (T). It is commonly expressed as PV = nRT, where R is the ideal gas constant, which can vary depending on the units of pressure, volume, and temperature used in the equation.

For students working with the ideal gas law, remember to pay attention to the units for each value. Pressure is often measured in atmospheres (atm) or torr; volume in liters (L); moles as the amount of substance; and temperature in Kelvin (K). Converting all the units to match (like torr to atm for pressure, or degrees Celsius to Kelvin for temperature) before starting any calculations is paramount for an accurate result.
Sublimation of Dry Ice
Sublimation is a fascinating process where a substance transitions directly from a solid to a gas without passing through the liquid state. Dry ice, which is solid carbon dioxide (CO2), is a common example of a substance that undergoes sublimation. When dry ice is exposed to air at room temperature, it sublimates and forms CO2 gas.

For students observing this phenomenon in an experiment, it's essential to note that the rate of sublimation depends on factors like temperature and air pressure. Your exercise may involve calculating the pressure exerted by the CO2 gas after sublimation鈥攖his is where understanding the ideal gas law comes in handy. If you're working on homework, ensure you know the initial mass of the dry ice to calculate the moles of CO2 gas produced, which are then used in the ideal gas law equation.
Molar Mass
Molar mass is the weight of one mole of a substance, typically measured in grams per mole (g/mol). This property is crucial for converting between the mass of a substance and the number of moles present鈥攁n indispensable step in stoichiometry and gas law calculations. To find the moles from a given mass, you would use the equation moles = mass / molar mass.

In practice, identifying the molar mass of CO2 (around 44.01 g/mol) allows for the calculation of moles of gas, which is essential when applying the ideal gas law. Students should be meticulous with their calculations and look up the correct molar mass for the relevant substance to avoid any errors.
Conversion of Temperature Units
Conversion of temperature units is a necessary step in many scientific calculations, especially when dealing with the ideal gas law. Since this law requires temperature to be in Kelvin, any temperatures given in Celsius or Fahrenheit must be converted before use.

For Celsius to Kelvin, the conversion formula is T(K) = T(掳C) + 273.15. This step must be performed accurately to ensure the correctness of your calculations. Keep in mind there is no such thing as 'negative' Kelvin, as the Kelvin scale starts at absolute zero鈥攖he coldest possible temperature.

Students often confuse temperature conversions, so a good tip is to double-check your converted values before plugging them into equations. Accurate conversion is fundamental to deriving the correct final pressure in gas law problems, just as done in the dry ice exercise.

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Most popular questions from this chapter

A 1.42 -g sample of helium and an unknown mass of \(\mathrm{O}_{2}\) are mixed in a flask at room temperature. The partial pressure of the helium is 42.5 torr, and that of the oxygen is 158 torr. What is the mass of the oxygen?

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains \(\mathrm{O}_{2}\) gas at a pressure of \(16,500 \mathrm{kPa}\) at \(23^{\circ} \mathrm{C}\) . (a) What mass of \(\mathrm{O}_{2}\) does the tank contain? (b) What volume would the gas occupy at STP? (c) At what temperature would the pressure in the tank equal 150.0 atm? (d) What would be the pressure of the gas, in kPa, if it were transferred to a container at \(24^{\circ} \mathrm{C}\) whose volume is 55.0 \(\mathrm{L}\) ?

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of \(\mathrm{Cl}_{2}\) gas is 8.70 \(\mathrm{L}\) at 895 torr and \(24^{\circ} \mathrm{C}\) .(a) How many grams of \(\mathrm{Cl}_{2}\) are in the sample? (b) What volume will the \(\mathrm{Cl}_{2}\) occupy at \(\mathrm{STP}\) ? (c) At what temperature will the volume be 15.00 \(\mathrm{L}\) if the pressure is \(8.76 \times 10^{2}\) torr? (d) At what pressure will the volume equal 5.00 L if the temperature is \(58^{\circ} \mathrm{C}\) ?

To minimize the rate of evaporation of the tungsten filament, \(1.4 \times 10^{-5}\) mol of argon is placed in a \(600-\mathrm{cm}^{3}\) light-bulb. What is the pressure of argon in the lightbulb at \(23^{\circ} \mathrm{C} ?\)

Ammonia and hydrogen chloride react to form solid ammonium chloride: $$\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$$ Two 2.00 -L flasks at \(25^{\circ} \mathrm{C}\) are connected by a valve, as shown in the drawing. One flask contains 5.00 \(\mathrm{g}\) of \(\mathrm{NH}_{3}(g),\) and the other contains 5.00 \(\mathrm{g}\) of \(\mathrm{HCl}(g) .\) When the valve is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.) (c) What mass of ammonium chloride will be formed?
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