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 743 torr 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 volume of CO₂ gas from liters to moles using the ideal gas law: PV = nRT. Remember to convert temperature to Kelvin and pressure to atmospheres.

Write the balanced chemical equations for the reactions of magnesium carbonate and calcium carbonate with hydrochloric acid, noting that both produce CO₂ gas.

Determine the total moles of CO₂ produced from the reactions using the ideal gas law calculation.

Set up a system of equations based on the stoichiometry of the reactions to relate the moles of CO₂ to the moles of magnesium carbonate and calcium carbonate in the mixture.

Solve the system of equations to find the mass of magnesium carbonate, then calculate the percentage by mass of magnesium carbonate in the original mixture.

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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.

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 essential for calculating the moles of carbon dioxide produced in the reaction, which is necessary for determining the composition of the original mixture.

Percentage by Mass

Percentage by mass is a way to express the concentration of a component in a mixture. It is calculated by dividing the mass of the component by the total mass of the mixture and multiplying by 100. In this problem, calculating the percentage by mass of magnesium carbonate requires determining its mass from the stoichiometric calculations and comparing it to the total mass of the sample.

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Gaseous iodine pentafluoride, IF5, can be prepared by the reaction of solid iodine and gaseous fluorine: I21s2 + 5 F21g2¡2 IF51g2 A 5.00-L flask containing 10.0 g of I2 is charged with 10.0 g of F2, and the reaction proceeds until one of the reagents is completely consumed. After the reaction is complete, the temperature in the flask is 125 °C. (a) What is the partial pressure of IF5 in the flask?

Gaseous iodine pentafluoride, IF5, can be prepared by the reaction of solid iodine and gaseous fluorine: I21s2 + 5 F21g2¡2 IF51g2 A 5.00-L flask containing 10.0 g of I2 is charged with 10.0 g of F2, and the reaction proceeds until one of the reagents is completely consumed. After the reaction is complete, the temperature in the flask is 125 °C. (d) What is the total mass of reactants and products in the flask?

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