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Ch.10 - Gases
Chapter 10, Problem 127c

A 6.53-g sample of a mixture of magnesium carbonate and calcium carbonate is treated with excess hydrochloric acid. The resulting reaction produces 1.72 L of carbon dioxide gas at 28 °C and 99.06 kPa pressure. (c) Assuming that the reactions are complete, calculate the percentage by mass of magnesium carbonate in the mixture.

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Convert the given volume of carbon dioxide (CO2) to moles using the ideal gas law equation: PV = nRT. Here, P is the pressure in atmospheres (convert from kPa to atm), V is the volume in liters, n is the number of moles of CO2, R is the gas constant (0.0821 L atm K^{-1} mol^{-1}), and T is the temperature in Kelvin (convert from °C to K).
Write the balanced chemical equations for the reaction of magnesium carbonate (MgCO3) and calcium carbonate (CaCO3) with hydrochloric acid (HCl). MgCO3 + 2 HCl -> MgCl2 + H2O + CO2 and CaCO3 + 2 HCl -> CaCl2 + H2O + CO2.
Determine the moles of CO2 produced from each carbonate. Since each mole of MgCO3 or CaCO3 produces one mole of CO2, the total moles of CO2 calculated from the ideal gas law equation equals the sum of the moles of MgCO3 and CaCO3 in the mixture.
Set up a system of equations based on the total mass of the mixture and the moles of each carbonate. Let x be the mass of MgCO3 and y be the mass of CaCO3 in the mixture. The equations are: x + y = 6.53 g (total mass of the mixture) and (molar mass of MgCO3)x + (molar mass of CaCO3)y = total moles of CO2 * molar mass of CO2.
Solve the system of equations to find the values of x and y. Then, calculate the percentage by mass of magnesium carbonate in the mixture using the formula: (mass of MgCO3 / total mass of mixture) * 100%.

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Key Concepts

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

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry will help relate the amount of carbon dioxide produced to the amounts of magnesium carbonate and calcium carbonate in the mixture.
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Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law is crucial for calculating the moles of carbon dioxide produced in the reaction, which will be used to find the mass of magnesium carbonate.
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Mass Percent Composition

Mass percent composition is a way to express the concentration of a component in a mixture as a percentage of the total mass. It is calculated by dividing the mass of the component by the total mass of the mixture and multiplying by 100. In this problem, determining the mass percent of magnesium carbonate requires knowing the mass of magnesium carbonate relative to the total mass of the sample.
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