/*! 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 64 A deep-sea diver uses a gas cyli... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 64

A deep-sea diver uses a gas cylinder with a volume of \(10.0 \mathrm{~L}\) and a content of \(51.2 \mathrm{~g}\) of \(\mathrm{O}_{2}\) and \(32.6 \mathrm{~g}\) of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is \(19^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The partial pressure of oxygen (O2) is \(P_{O2} = 66.62 \mathrm{~kPa}\), the partial pressure of helium (He) is \(P_{He} = 169.14 \mathrm{~kPa}\), and the total pressure is \(P_{total} = 235.76 \mathrm{~kPa}\).

Step by step solution

01

Convert mass to moles

First, we need to convert the mass of each of the gases to moles. We can do this by dividing the mass of each gas by its respective molar mass. For oxygen (O2): Molar mass of O2: \(\mathrm{M_{O2}} = 32~g/mol\) Number of moles of O2: \(n_{O2} =\frac{51.2 \mathrm{~g}}{32 \mathrm{~g/mol}} \) For helium (He): Molar mass of He: \(\mathrm{M_{He}} = 4~g/mol\) Number of moles of He: \(n_{He} =\frac{32.6 \mathrm{~g}}{4 \mathrm{~g/mol}} \)
02

Apply Ideal Gas Law to find partial pressure of each gas

Now, we can use the ideal gas law to find the partial pressure of each gas inside the cylinder. Ideal Gas Law: \(PV = nRT\) Where: P = pressure V = volume n = number of moles R = Ideal Gas Constant, \(8.314 \mathrm{J/(mol \cdot K)}\) T = temperature in Kelvin We need to convert the temperature given in Celsius to Kelvin: \(T_K = T_C + 273.15\) For oxygen (O2): \(P_{O2}V = n_{O2}RT\) \(P_{O2} = \frac{n_{O2}RT}{V}\) For helium (He): \(P_{He}V = n_{He}RT\) \(P_{He} = \frac{n_{He}RT}{V}\)
03

Calculate the total pressure

According to Dalton's Law of Partial Pressures, the total pressure in the cylinder is equal to the sum of the partial pressures of each gas. Total Pressure (P_total) = \(P_{O2} + P_{He}\)
04

Substitute values and calculate

Now, we can substitute the known values into the equations and calculate the partial pressures of each gas and the total pressure. For oxygen (O2): \(P_{O2} = \frac{(\frac{51.2 \mathrm{~g}}{32 \mathrm{~g/mol}})(8.314 \mathrm{J/(mol \cdot K)})(19 + 273.15 \mathrm{~K})}{10.0 \mathrm{~L}}\) Calculate \(P_{O2}\). For helium (He): \(P_{He} = \frac{(\frac{32.6 \mathrm{~g}}{4 \mathrm{~g/mol}})(8.314 \mathrm{J/(mol \cdot K)})(19 + 273.15 \mathrm{~K})}{10.0 \mathrm{~L}}\) Calculate \(P_{He}\). Total Pressure (P_total) = \(P_{O2} + P_{He}\) Calculate the total pressure, \(P_{total}\).

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Most popular questions from this chapter

Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and has a boiling point at atmospheric pressure of \(-164^{\circ} \mathrm{C}\). One possible strategy is to oxidize the methane to methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), which has a boiling point of \(65^{\circ} \mathrm{C}\) and can therefore be shipped more readily. Suppose that \(10.7 \times 10^{9} \mathrm{ft}^{3}\) of methane at atmospheric pressure and \(25^{\circ} \mathrm{C}\) is oxidized to methanol. (a) What volume of methanol is formed if the density of \(\mathrm{CH}_{3} \mathrm{OH}\) is \(0.791 \mathrm{~g} / \mathrm{mL}\) ? (b) Write balanced chemical equations for the oxidations of methane and methanol to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). Calculate the total enthalpy change for complete combustion of the \(10.7 \times 10^{9} \mathrm{ft}^{3}\) of methane just described and for complete combustion of the equivalent amount of methanol, as calculated in part (a). (c) Methane, when liquefied, has a density of \(0.466 \mathrm{~g} / \mathrm{mL}\); the density of methanol at \(25^{\circ} \mathrm{C}\) is \(0.791 \mathrm{~g} / \mathrm{mL}\). Compare the enthalpy change upon combustion of a unit volume of liquid methane and liquid methanol. From the standpoint of energy production, which substance has the higher enthalpy of combustion per unit volume?

A fixed quantity of gas at \(21^{\circ} \mathrm{C}\) exhibits a pressure of 752 torr and occupies a volume of \(5.12 \mathrm{~L}\). (a) Calculate the volume the gas will occupy if the pressure is increased to \(1.88 \mathrm{~atm}\) while the temperature is held constant. (b) Calculate the volume the gas will occupy if the temperature is increased to \(175^{\circ} \mathrm{C}\) while the pressure is held constant.

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Hurricane Wilma of 2005 is the most intense hurricane on record in the Atlantic basin, with a low-pressure reading of 882 mbar (millibars). Convert this reading into (a) atmospheres, (b) torr, and (c) inches of \(\mathrm{Hg}\) -

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In \(1 \mathrm{hr}\) the average cockroach running at \(0.08 \mathrm{~km} / \mathrm{hr}\) consumed \(0.8 \mathrm{~mL}\) of \(\mathrm{O}_{2}\) at 1 atm pressure and \(24^{\circ} \mathrm{C}\) per gram of insect mass. (a) How many moles of \(\mathrm{O}_{2}\) would be consumed in \(1 \mathrm{hr}\) by a \(5.2-\mathrm{g}\) cockroach moving at this speed? (b) This same cockroach is caught by a child and placed in a 1-qt fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, will the cockroach consume more than \(20 \%\) of the available \(\mathrm{O}_{2}\) in a 48-hr period? (Air is \(21 \mathrm{~mol} \% \mathrm{O}_{2}\).)
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