Ch.3 - Chemical Reactions and Reaction Stoichiometry

Problem 97

Chapter 3, Problem 97

A compound, Na2Cr2Ox, where x is unknown, is analyzed and found to contain 39.70% Cr. What is the value of x?

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Determine the molar masses of Na (Sodium), Cr (Chromium), and O (Oxygen) using the periodic table. The molar mass of Na is approximately 22.99 g/mol, Cr is approximately 52.00 g/mol, and O is approximately 16.00 g/mol.

Calculate the total mass of Chromium in the compound Na2Cr2Ox by using the given percentage of Cr (39.70%). Assume a 100 g sample of the compound, which means it contains 39.70 g of Cr.

Using the molar mass of Cr, convert the mass of Cr (39.70 g) to moles of Cr. This is done by dividing the mass of Cr by its molar mass (52.00 g/mol).

Calculate the molar mass of the rest of the compound (Na2 and Ox) by subtracting the mass of Cr from the total mass of the compound (100 g). Then, use the molar masses of Na and O to find the number of moles of Na and O in the compound.

Set up an equation based on the stoichiometry of the compound Na2Cr2Ox, where the moles of Na and Cr are known, and solve for x, the number of moles of O, to satisfy the compound's formula and mass balance.

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Key Concepts

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

Molar Mass and Percent Composition

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. Percent composition refers to the percentage by mass of each element in a compound. To find the unknown 'x' in Na2Cr2Ox, we need to use the percent composition of chromium (Cr) to relate it to the total molar mass of the compound.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. In this context, it allows us to set up a relationship between the moles of chromium and the total moles of the compound, helping to determine the unknown variable 'x' by using the known percentage of chromium.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of elements in a compound. By determining the moles of each element in Na2Cr2Ox based on the percent composition, we can derive the empirical formula, which will help us find the value of 'x' by ensuring the ratio of sodium, chromium, and oxygen is consistent with the given data.

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