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Chapter 3: Problem 51

What is the molecular formula of each of the following compounds? $$ \begin{array}{l}{\text { (a) empirical formula } \mathrm{CH}_{2}, \text { molar mass }=84.0 \mathrm{g} / \mathrm{mol}} \\ {\text { (b) empirical formula } \mathrm{NH}_{2} \mathrm{Cl} \text { , molar mass }=51.5 \mathrm{g} / \mathrm{mol}}\end{array} $$

Short Answer

Expert verified
The molecular formulas for the given compounds are: (a) C_6H_{12} (b) NH_2Cl

Step by step solution

01

Calculate the molar mass of the empirical formula

Using the periodic table, find the molar mass of the elements present in the empirical formula CH_2. C: 12.01 g/mol H: 1.008 g/mol Total molar mass of CH2 = 12.01 + (2 x 1.008) = 14.026 g/mol
02

Determine the ratio between the given molar mass and the empirical formula's molar mass

The given molar mass of compound (a) is 84.0 g/mol. Divide the given molar mass by the empirical formula's molar mass: Ratio = \(\frac{84.0}{14.026}\) ≈ 6
03

Multiply the empirical formula by the ratio determined in step 2 to get the molecular formula

Since the ratio is 6, the molecular formula will be six times the empirical formula: Molecular formula = (CH_2) x 6 = C_6H_{12} The molecular formula of compound (a) is C_6H_{12}. For Compound (b):
04

Calculate the molar mass of the empirical formula

Using the periodic table, find the molar mass of the elements present in the empirical formula NH_2Cl. N: 14.01 g/mol H: 1.008 g/mol Cl: 35.45 g/mol Total molar mass of NH_2Cl = 14.01 + (2 x 1.008) + 35.45 = 51.476 g/mol
05

Determine the ratio between the given molar mass and the empirical formula's molar mass

The given molar mass of compound (b) is 51.5 g/mol. Divide the given molar mass by the empirical formula's molar mass: Ratio = \(\frac{51.5}{51.476}\) ≈ 1
06

Multiply the empirical formula by the ratio determined in step 2 to get the molecular formula

Since the ratio is 1, the molecular formula will be the same as the empirical formula: Molecular formula = NH_2Cl The molecular formula of compound (b) is NH_2Cl.

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Most popular questions from this chapter

Serotonin is a compound that conducts nerve impulses in the brain. It contains \(68.2 \% \mathrm{C}, 6.86 \% \mathrm{H}, 15.9 \% \mathrm{N},\) and 9.08\(\% \mathrm{O}\) . Its molar mass is 176 \(\mathrm{g} / \mathrm{mol} .\) Determine its molecular formula.

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I)oxide decomposes into silver metal and oxygen gas when heated; (c) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air; (d) methyl tert- butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

Determine the empirical formulas of the compounds with the following compositions by mass: $$ \begin{array}{l}{\text { (a) } 55.3 \% \mathrm{K}, 14.6 \% \mathrm{P}, \text { and } 30.1 \% \mathrm{O}} \\ {\text { (b) } 24.5 \% \mathrm{Na}, 14.9 \% \mathrm{Si}, \text { and } 60.6 \% \mathrm{F}} \\ {\text { (c) } 62.1 \% \mathrm{C}, 5.21 \% \mathrm{H}, 12.1 \% \mathrm{N}, \text { and the remainder O }}\end{array} $$

An iron ore sample contains \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) together with other substances. Reaction of the ore with CO produces iron metal: $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) $$ (a) Balance this equation. (b) Calculate the number of grams of CO that can react with 0.350 \(\mathrm{kg}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) . (c) Calculate the number of grams of Fe and the number of grams of \(\mathrm{CO}_{2}\) formed when 0.350 \(\mathrm{kg}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) reacts. (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

Without doing any detailed calculations (but using a periodic table to give atomic weights, rank the following samples in order of increasing numbers of atoms: 42 gof NaHCO \(_{3}, 1.5 \mathrm{mol} \mathrm{CO}_{2}, 6.0 \times 10^{24} \mathrm{Ne}\) atoms.
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