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Chapter 3: Problem 52

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{HCO}_{2}\), molar mass \(=90.0 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\), molar mass \(=88 \mathrm{~g} / \mathrm{mol}\)

Short Answer

Expert verified
The molecular formulas for the given compounds are: (a) \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\) (b) \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\)

Step by step solution

01

Calculate the molar mass of the empirical formula

The empirical formula is given as \(\mathrm{HCO}_{2}\). To find its molar mass, look up the molar masses of each individual element and add them together: - H: 1.01 g/mol - C: 12.01 g/mol - O: 16.00 g/mol Molar mass of \(\mathrm{HCO}_{2}\) = (1.01 + 12.01 + (2 脳 16.00)) g/mol = 45.02 g/mol.
02

Find the ratio between the molar masses of the molecular and empirical formulas

Divide the given molar mass of the molecular formula (90.0 g/mol) by the molar mass of the empirical formula (45.02 g/mol) to find the ratio: Ratio = \(\frac{90.0}{45.02} \approx 2\).
03

Multiply the empirical formula by the ratio found in step 2

Since the ratio is 2, we need to multiply each element in the empirical formula by 2: Molecular formula = \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\). (b)
04

Calculate the molar mass of the empirical formula

The empirical formula is given as \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\). To find its molar mass, look up the molar masses of each individual element and add them together: - C: 12.01 g/mol - H: 1.01 g/mol - O: 16.00 g/mol Molar mass of \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) = (2 脳 12.01 + 4 脳 1.01 + 16.00) g/mol = 44.06 g/mol.
05

Find the ratio between the molar masses of the molecular and empirical formulas

Divide the given molar mass of the molecular formula (88 g/mol) by the molar mass of the empirical formula (44.06 g/mol) to find the ratio: Ratio = \(\frac{88}{44.06} \approx 2\).
06

Multiply the empirical formula by the ratio found in step 2

Since the ratio is 2, we need to multiply each element in the empirical formula by 2: Molecular formula = \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\).

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Most popular questions from this chapter

(a) What is the mass, in grams, of \(2.50 \times 10^{-3} \mathrm{~mol}\) of ammonium phosphate? (b) How many moles of chloride ions are in \(0.2550 \mathrm{~g}\) of aluminum chloride? (c) What is the mass, in grams, of \(7.70 \times 10^{20}\) molecules of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\) ? (d) What is the molar mass of cholesterol if \(0.00105 \mathrm{~mol}\) has a mass of \(0.406 \mathrm{~g}\) ?

A particular coal contains \(2.5 \%\) sulfur by mass. When this coal is burned at a power plant, the sulfur is converted into sulfur dioxide gas, which is a pollutant. To reduce sulfur dioxide emissions, calcium oxide (lime) is used. The sulfur dioxide reacts with calcium oxide to form solid calcium sulfite. (a) Write the balanced chemical equation for the reaction. (b) If the coal is burned in a power plant that uses 2000 tons of coal per day, what mass of calcium oxide is required daily to eliminate the sulfur dioxide? (c) How many grams of calcium sulfite are produced daily by this power plant?

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), in the atmosphere in a chemical plant is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). How many moles of vinyl chloride in each liter does this represent? How many molecules per liter?

The molecular formula of aspartame, the artificial sweetener marketed as NutraSweet \({ }^{\infty}\), is \(\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{5}\). (a) What is the molar mass of aspartame? (b) How many moles of aspartame are present in \(1.00 \mathrm{mg}\) of aspartame? (c) How many molecules of aspartame are present in \(1.00 \mathrm{mg}\) of aspartame? (d) How many hydrogen atoms are present in \(1.00 \mathrm{mg}\) of aspartame?

The fizz produced when an Alka-Seltzer tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) : $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+& \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment \(1.00 \mathrm{~g}\) of sodium bicarbonate and \(1.00 \mathrm{~g}\) of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?
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