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Chapter 3: Problem 96

A sample of a compound of \(\mathrm{Cl}\) and \(\mathrm{O}\) reacts with an excess of \(\mathrm{H}_{2}\) to give \(0.233 \mathrm{~g}\) of \(\mathrm{HCl}\) and \(0.403 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\). Determine the empirical formula of the compound.

Short Answer

Expert verified
The empirical formula of the compound is \(ClO_7\).

Step by step solution

01

Calculate the moles of Cl

From the balanced reaction, we know that 1 mol of \(\mathrm{HCl}\) has 1 mol of \(\mathrm{Cl}\). To calculate the moles of \(\mathrm{Cl}\), we use the molar mass of \(\mathrm{HCl}\) which is \(36.461 \mathrm{~g/mol}\) from the periodic table. So, moles of \(\mathrm{Cl}\) = mass of \(\mathrm{HCl}\) / molar mass of \(\mathrm{HCl}\) = \(0.233 \mathrm{~g}\) / \(36.461 \mathrm{~g/mol}\) = \(0.00639 \mathrm{~mol}\) (rounded to 5 decimal places)
02

Calculate the moles of O

Following similar steps to Step 1, we calculate the moles of \(\mathrm{O}\) by dividing the mass of \(\mathrm{H2O}\) by the molar mass of \(\mathrm{H2O}\), \(18.015 \mathrm{~g/mol}\). So, moles of \(\mathrm{O}\) = mass of \(\mathrm{H2O}\) / molar mass of \(\mathrm{H2O}\) = \(0.403 \mathrm{~g}\) / \(18.015 \mathrm{~g/mol}\) = \(0.02238 \mathrm{~mol}\) (rounded to 5 decimal places)
03

Determine the simplest whole number ratio

The empirical formula is the simplest ratio of moles of each element. Thus, calculate the ratio of moles of Cl to O by dividing the moles of each by the smallest number of moles calculated. Ratio of Cl:O = moles of Cl / smallest moles = \(0.00639 / 0.00639\): moles of O / smallest moles = \(0.02238 / 0.00639\) = 3.5. This is a ratio of 1:3.5 but empirical formulas need to be in whole numbers. Multiplying by 2 gives the whole number ratio 1:7, so the empirical formula is \(ClO_7\).

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Most popular questions from this chapter

A reaction having a 90 percent yield may be considered a successful experiment. However, in the synthesis of complex molecules such as chlorophyll and many anticancer drugs, a chemist often has to carry out multiple-step synthesis. What is the overall percent yield for such a synthesis, assuming it is a 30 -step reaction with a 90 percent yield at each step?

What is the mass (in amu) of a carbon-12 atom? Why is the atomic mass of carbon listed as 12.01 amu in the table on the inside front cover of this book?

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2} ?\)

What are the empirical formulas of the compounds with the following compositions? (a) 2.1 percent \(\mathrm{H}\), 65.3 percent \(\mathrm{O}, 32.6\) percent \(\mathrm{S}\) (b) 20.2 percent \(\mathrm{Al}\), 79.8 percent \(\mathrm{Cl}\)

Why is the theoretical yield of a reaction determined only by the amount of the limiting reagent?
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