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Chapter 3: Problem 110

In an experiment, \(244 \mathrm{mL}\) of chlorine gas \(\left(\mathrm{Cl}_{2}, d=2.898 \mathrm{g} / \mathrm{L}\right)\) combines with iodine to give \(1.553 \mathrm{g}\) of a binary compound. In a separate experiment, the molar mass of the compound is found to be about \(467 \mathrm{g} / \mathrm{mol} .\) What is the molecular formula of this compound?

Short Answer

Expert verified
The molecular formula of the compound is \(\mathrm{Cl}_x\mathrm{I}_y\). The exact values of x and y can be found by following the above steps.

Step by step solution

01

Calculate moles of chlorine

Using the density formula \(d = m/v\), rearrange it as \(m = d \times v\) to calculate the mass of chlorine. Given that the molar mass of chlorine (\(\mathrm{Cl}_{2}\)) is 70.90 g/mol, divide the mass by the molar mass to get the number of moles.
02

Calculate moles of iodine

From the experiment, it's given that 1.553 g of a compound is created. Given that this is a binary compound with chlorine and iodine, subtract the mass of chlorine calculated in Step 1 from 1.553 g to get the mass of iodine. Divide this by the molar mass of iodine (126.90 g/mol) to calculate the number of moles of iodine.
03

Find ratio of chlorine to iodine

Divide the number of moles of chlorine by the moles of iodine to find the ratio of chlorine to iodine in the compound.
04

Determine molecular formula

The molecular formula is represented as \(\mathrm{Cl}_x\mathrm{I}_y\), where \(x\) and \(y\) are the ratio found in Step 3. Take into consideration that the molar mass of the compound from a separate experiment is given as 467 g/mol, which will help to find the values of x and y and hence the molecular formula.

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