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Chapter 5: Problem 98

A tank contains a mixture of 52.5 g oxygen gas and 65.1 \(\mathrm{g}\) carbon dioxide gas at \(27^{\circ} \mathrm{C}\) . The total pressure in the tank is 9.21 atm. Calculate the partial pressures of each gas in the container.

Short Answer

Expert verified
The partial pressures of oxygen and carbon dioxide in the container are \(4.84 \: \text{atm}\) and \(4.37 \: \text{atm}\), respectively.

Step by step solution

01

Convert mass to moles

First, we need to convert the given mass of each gas to moles using the molar mass of each gas. The molar mass of oxygen (O₂) is 32 g/mol, and the molar mass of carbon dioxide (CO₂) is 44 g/mol. For Oxygen: moles of O₂ = mass of O₂ / molar mass of O₂ moles of O₂ = 52.5 g / 32 g/mol = 1.64 mol For Carbon dioxide: moles of CO₂ = mass of CO₂ / molar mass of CO₂ moles of CO₂ = 65.1 g / 44 g/mol = 1.48 mol
02

Calculate total moles and mole fractions

Next, we need to find the total moles of both gases combined, and then calculate the mole fraction for each gas. Total moles = moles of O₂ + moles of CO₂ Total moles = 1.64 mol + 1.48 mol = 3.12 mol Now, we can find the mole fraction for each gas: Mole fraction of O₂ = moles of O₂ / total moles = 1.64 mol / 3.12 mol = 0.526 Mole fraction of CO₂ = moles of CO₂ / total moles = 1.48 mol / 3.12 mol = 0.474
03

Calculate partial pressures using Dalton's Law

Now we can use Dalton's Law of Partial Pressures, where the partial pressure of each gas equals the product of the total pressure and the mole fraction of that gas: Partial pressure of O₂ = total pressure * mole fraction of O₂ Partial pressure of O₂ = 9.21 atm * 0.526 = 4.84 atm Partial pressure of CO₂ = total pressure * mole fraction of CO₂ Partial pressure of CO₂ = 9.21 atm * 0.474 = 4.37 atm The partial pressures of oxygen and carbon dioxide in the container are 4.84 atm and 4.37 atm, respectively.

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Most popular questions from this chapter

One of the chemical controversies of the nineteenth century concerned the element beryllium (Be). Berzelius originally claimed that beryllium was a trivalent element (forming \(\mathrm{Be}^{3+}\) ions) and that it gave an oxide with the formula \(\mathrm{Be}_{2} \mathrm{O}_{3}\) . This resulted in a calculated atomic mass of 13.5 for beryllium. In formulating his periodic table, Mendeleev proposed that beryllium was divalent (forming \(\mathrm{Be}^{2+}\) ions) and that it gave an oxide with the formula BeO. This assumption gives an atomic mass of \(9.0 .\) In \(1894,\) A. Combes (Comptes Rendus \(1894,\) p. 1221 ) reacted beryllium with the anion $C_{5} \mathrm{H}_{7} \mathrm{O}_{2}^{-}$ and measured the density of the gaseous product. Combes's data for two different experiments are as follows: $$\begin{array}{lll}{\text { Mass }} & {0.2022 \mathrm{g}} & {0.2224 \mathrm{g}} \\ {\text { Volume }} & {22.6 \mathrm{cm}^{3}} & {26.0 \mathrm{cm}^{3}} \\ {\text { Temperature }} & {13^{\circ} \mathrm{C}} & {17^{\circ} \mathrm{C}} \\ {\text { Pressure }} & {765.2 \mathrm{mm} \mathrm{Hg}} & {764.6 \mathrm{mm}}\end{array}$$ If beryllium is a divalent metal, the molecular formula of the product will be \(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{2} ;\) if it is trivalent, the formula will be $\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{3} .$ Show how Combes's data help to confirm that beryllium is a divalent metal.

The partial pressure of \(\mathrm{CH}_{4}(g)\) is 0.175 atm and that of \(\mathrm{O}_{2}(g)\) is 0.250 \(\mathrm{atm}\) in a mixture of the two gases. a. What is the mole fraction of each gas in the mixture? b. If the mixture occupies a volume of 10.5 \(\mathrm{L}\) at $65^{\circ} \mathrm{C}$ , calculate the total number of moles of gas in the mixture. c. Calculate the number of grams of each gas in the mixture.

Consider the following reaction: $$4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)$$ It takes 2.00 L of pure oxygen gas at STP to react completely with a certain sample of aluminum. What is the mass of aluminum reacted?

Consider a children’s cartoon illustrating a child holding the strings of several helium balloons and being lifted into the sky. a. Estimate the minimum number of 10.-L balloons it would take to lift a 50.-lb child. Assume air has an average molar mass of 29 g/mol, and assume the masses of the balloons and strings are negligible. b. Explain why the balloons can lift the child.

A 2.50-L container is filled with 175 g argon. a. If the pressure is 10.0 atm, what is the temperature? b. If the temperature is 225 K, what is the pressure?
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