Ch.6 - Gases

Problem 107

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Chapter 6, Problem 107

The mass of an evacuated 255 mL flask is 143.187 g. The mass of the flask filled with 267 torr of an unknown gas at 25 °C is 143.289 g. Calculate the molar mass of the unknown gas.

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Calculate the mass of the unknown gas by subtracting the mass of the evacuated flask from the mass of the flask filled with the gas: \( \text{mass of gas} = 143.289 \text{ g} - 143.187 \text{ g} \).

Convert the pressure from torr to atm using the conversion factor: \( 1 \text{ atm} = 760 \text{ torr} \).

Convert the temperature from Celsius to Kelvin using the formula: \( T(\text{K}) = T(\text{°C}) + 273.15 \).

Use the ideal gas law \( PV = nRT \) to solve for the number of moles \( n \) of the gas, where \( P \) is the pressure in atm, \( V \) is the volume in liters, \( R \) is the ideal gas constant \( 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \), and \( T \) is the temperature in Kelvin.

Calculate the molar mass of the gas using the formula: \( \text{Molar mass} = \frac{\text{mass of gas}}{n} \), where \( n \) is the number of moles calculated in the previous step.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions and is used to derive the molar mass of a gas when its pressure, volume, and temperature are known.

Molar Mass Calculation

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the molar mass of the unknown gas, the mass difference between the empty flask and the flask filled with gas is divided by the number of moles of gas, which can be determined using the Ideal Gas Law.

Gas Density

Gas density is the mass of a gas per unit volume, often expressed in grams per liter (g/L). In this problem, the density of the unknown gas can be derived from the mass of the gas and the volume of the flask, which is crucial for calculating the molar mass using the relationship between density, molar mass, and the Ideal Gas Law.

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Related Practice

Use the van der Waals equation and the ideal gas equation to calculate the pressure exerted by 1.000 mol of Cl₂ in a volume of 5.000 L at a temperature of 273.0 K. Explain why the two values are different.

Modern pennies are composed of zinc coated with copper. A student determines the mass of a penny to be 2.482 g and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved): Zn(s) + 2 HCl(aq)¡ H2( g) + ZnCl2(aq) The student collects the hydrogen produced over water at 25 °C. The collected gas occupies a volume of 0.899 L at a total pressure of 791 mmHg. Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.)

A 2.85-g sample of an unknown chlorofluorocarbon decomposes and produces 564 mL of chlorine gas at a pressure of 752 mmHg and a temperature of 298 K. What is the percent chlorine (by mass) in the unknown chlorofluorocarbon?

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Textbook Question

A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 82.66% carbon and 17.34% hydrogen by mass. The mass of 158 mL of the gas, measured at 556 mmHg and 25 °C, was 0.275 g. What is the molecular formula of the compound?

A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 85.63% C and 14.37% H by mass. The mass of 258 mL of the gas, measured at STP, was 0.646 g. What is the molecular formula of the compound?

Consider the reaction: 2 Ag₂O(s) → 4 Ag(s) + O₂(g) If this reaction produces 15.8 g of Ag(s), what total volume of gas can be collected over water at a temperature of 25 °C and a total pressure of 752 mmHg?

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