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Chapter 8: Problem 15

The molecular formula of a compound is \(\mathrm{X}_{4} \mathrm{O}_{9}\). If the compound contains \(40 \% \mathrm{X}\), by mass, what is the atomic mass of \(X\) ? (a) 24 (b) 12 (c) 26 (d) 13

Short Answer

Expert verified
Question: Determine the atomic mass of element X in the molecular formula X4O9, given that the mass percentage of X in the compound is 40%. Answer: (a) 24

Step by step solution

01

Determine the mass percentage of oxygen

Since the compound only contains two elements, \(X\) and oxygen (O), the mass percentage of oxygen is 100% - mass percentage of \(X\). Given that the mass percentage of \(X\) is 40%, the mass percentage of oxygen is 60% (100% - 40%).
02

Convert mass percentages to grams

For simpler calculations, we can assume that we have a 100 gram sample of the compound. In this sample, 40 grams would be \(X\) and 60 grams would be oxygen.
03

Determine the moles of each element

To determine the moles of each element, divide the mass of each element by its atomic mass. The atomic mass of oxygen is 16 grams/mol. So, there are 60/16 = 3.75 moles of oxygen in the 100 gram sample.
04

Determine the molar ratio of the elements in the molecular formula

The molecular formula of the compound is \(\mathrm{X}_{4} \mathrm{O}_{9}\). From this, we can determine that the molar ratio of \(X\) to oxygen in the molecular formula is 4:9.
05

Divide moles of oxygen by the molar ratio

Divide the moles of oxygen (3.75) by the molar ratio of oxygen in the molecular formula (9). This result represents the 'mole unit' for the compound. 3.75/9 = 0.4167 'mole units' for the compound.
06

Determine the moles of X using the 'mole unit'

Multiply the 'mole unit' obtained in Step 5 (0.4167) by the molar ratio of \(X\) in the molecular formula (4). This result represents the moles of \(X\) in the 100 gram sample. 0.4167 * 4 = 1.6667 moles of \(X\)
07

Calculate the atomic mass of X

Divide the mass of \(X\) (40 grams) by the moles of \(X\) (1.6667) to find the atomic mass of \(X\). Atomic mass of \(X\) = 40 / 1.6667 = 24 The atomic mass of \(X\) is 24, which corresponds to option (a).

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Most popular questions from this chapter

A quantity of \(0.2 \mathrm{~g}\) of an organic compound containing, \(\mathrm{C}, \mathrm{H}\) and \(\mathrm{O}\), on combustion yielded \(0.147 \mathrm{~g} \mathrm{CO}_{2}\) and \(0.12 \mathrm{~g}\) water. The percentage of oxygen in it is (a) \(73.29 \%\) (b) \(78.45 \%\) (c) \(83.23 \%\) (d) \(89.50 \%\)

The commonly used pain reliever, aspirin, has the molecular formula \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .\) If a sample of aspirin contains \(0.968 \mathrm{~g}\) of carbon, what is the mass of hydrogen in the sample? (a) \(0.717 \mathrm{~g}\) (b) \(0.0717 \mathrm{~g}\) (c) \(8.000 \mathrm{~g}\) (d) \(0.645 \mathrm{~g}\)

An amount of \(1.0 \times 10^{-3}\) moles of \(\mathrm{Ag}^{+}\) and \(1.0 \times 10^{-3}\) moles of \(\mathrm{CrO}_{4}^{2-}\) reacts together to form solid \(\mathrm{Ag}_{2} \mathrm{CrO}_{4} \cdot\) What is the amount of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) formed? \((\mathrm{Ag}=108, \mathrm{Cr}=52)\) (a) \(0.332 \mathrm{~g}\) (b) \(0.166 \mathrm{~g}\) (c) \(332 \mathrm{~g}\) (d) \(166 \mathrm{~g}\)

An aqueous solution of glucose is \(10 \%\) \((\mathrm{w} / \mathrm{v}) .\) The volume in which \(1 \mathrm{~mole}\) of glucose is dissolved, will be (a) 181 (b) 91 (c) \(0.91\) (d) \(1.81\)

For \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\), which is the correct mole relationship? (a) \(9 \times\) mole of \(\mathrm{Cu}=\) mole of \(\mathrm{O}\) (b) \(5 \times\) mole of \(\mathrm{Cu}=\) mole of \(\mathrm{O}\) (c) \(9 \times\) mole of \(\mathrm{Cu}=\) mole of \(\mathrm{O}_{2}\) (d) mole of \(\mathrm{Cu}=5 \times\) mole of \(\mathrm{O}\)
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