Disilane, Si2Hx, is analyzed and found to contain 90.28% silicon by mass. What is the value of x?

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Step 1: Understand that the problem is asking for the number of hydrogen atoms in the molecule of disilane. The percentage composition of silicon in the molecule is given, and we know that the rest of the mass must be due to hydrogen.

Step 2: Calculate the percentage composition of hydrogen in the molecule. Since the total mass percentage in a molecule is always 100%, the mass percentage of hydrogen is 100% - 90.28% = 9.72%.

Step 3: Convert the mass percentages to grams (assuming we have 100g of the compound, so the percentages are equivalent to grams). This gives us 90.28g of silicon and 9.72g of hydrogen.

Step 4: Convert the masses of silicon and hydrogen to moles by dividing by their respective atomic masses. The atomic mass of silicon (Si) is approximately 28.09 g/mol and the atomic mass of hydrogen (H) is approximately 1.01 g/mol.

Step 5: The ratio of moles of hydrogen to moles of silicon gives the value of x in the formula Si2Hx. This is because the subscript in a chemical formula represents the number of atoms of that element in the molecule, which is proportional to the number of moles of that element in a sample of the compound.

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Key Concepts

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

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a chemical formula. For disilane, Si2Hx, the molar mass will depend on the number of hydrogen atoms (x) and the atomic masses of silicon and hydrogen.

Mass Percent Composition

Mass percent composition is the percentage by mass of each element in a compound. It is calculated by dividing the mass of the element in the compound by the total mass of the compound and multiplying by 100. In this case, knowing that disilane contains 90.28% silicon by mass allows us to set up an equation to find the value of x.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. It involves using mole ratios derived from balanced chemical equations to relate quantities of substances. In this problem, stoichiometry helps us relate the mass of silicon to the mass of hydrogen in disilane to solve for x.

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