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Chapter 3: Problem 46

Determine the empirical formulas of the compounds with the following compositions by mass: (a) \(55.3 \% \mathrm{~K}, 14.6 \% \mathrm{P}\), and \(30.1 \% \mathrm{O}\) (b) \(24.5 \% \mathrm{Na}, 14.9 \% \mathrm{Si}\), and \(60.6 \% \mathrm{~F}\) (c) \(62.1 \% \mathrm{C}, 5.21 \% \mathrm{H}, 12.1 \% \mathrm{~N}\), and \(20.7 \% \mathrm{O}\)

Short Answer

Expert verified
The empirical formulas for the given compounds are: (a) K鈧働O鈧� (b) Na鈧係iF鈧� (c) 颁鈧佲倐贬鈧佲倐狈鈧侽鈧�

Step by step solution

01

Convert percentages to grams

Assume 100g of sample, as it does not affect the final result: K: 55.3g P: 14.6g O: 30.1g
02

Convert grams to moles

K: \(\frac{55.3 \text{g}}{39.10 \frac{\text{g}}{\text{mol}}} = 1.414 \text{mol}\) P: \(\frac{14.6 \text{g}}{30.97 \frac{\text{g}}{\text{mol}}} = 0.471 \text{mol}\) O: \(\frac{30.1 \text{g}}{16.00 \frac{\text{g}}{\text{mol}}} = 1.881 \text{mol}\)
03

Divide by the smallest moles value

K: \(\frac{1.414}{0.471}\) 鈮� 3 P: \(\frac{0.471}{0.471}\) 鈮� 1 O: \(\frac{1.881}{0.471}\) 鈮� 4
04

Create the empirical formula

K鈧働O鈧� #(b) 24.5% Na, 14.9% Si, and 60.6% F#
05

Convert percentages to grams

Assume 100g of sample: Na: 24.5g Si: 14.9g F: 60.6g
06

Convert grams to moles

Na: \(\frac{24.5 \text{g}}{22.99 \frac{\text{g}}{\text{mol}}} = 1.065 \text{mol}\) Si: \(\frac{14.9 \text{g}}{28.09 \frac{\text{g}}{\text{mol}}} = 0.530 \text{mol}\) F: \(\frac{60.6 \text{g}}{19.00 \frac{\text{g}}{\text{mol}}} = 3.189 \text{mol}\)
07

Divide by the smallest moles value

Na: \(\frac{1.065}{0.530}\) 鈮� 2 Si: \(\frac{0.530}{0.530}\) 鈮� 1 F: \(\frac{3.189}{0.530}\) 鈮� 6
08

Create the empirical formula

Na鈧係iF鈧� #(c) 62.1% C, 5.21% H, 12.1% N, and 20.7% O#
09

Convert percentages to grams

Assume 100g of sample: C: 62.1g H: 5.21g N: 12.1g O: 20.7g
10

Convert grams to moles

C: \(\frac{62.1 \text{g}}{12.01 \frac{\text{g}}{\text{mol}}} = 5.171 \text{mol}\) H: \(\frac{5.21 \text{g}}{1.01 \frac{\text{g}}{\text{mol}}} = 5.158 \text{mol}\) N: \(\frac{12.1 \text{g}}{14.01 \frac{\text{g}}{\text{mol}}} = 0.863 \text{mol}\) O: \(\frac{20.7 \text{g}}{16.00 \frac{\text{g}}{\text{mol}}} = 1.294 \text{mol}\)
11

Divide by the smallest moles value

C: \(\frac{5.171}{0.863}\) 鈮� 6 H: \(\frac{5.158}{0.863}\) 鈮� 6 N: \(\frac{0.863}{0.863}\) 鈮� 1 O: \(\frac{1.294}{0.863}\) 鈮� 1.5 Since we obtained 1.5 instead of whole numbers, we should multiply all values by 2 to get integers: C: 6 脳 2 = 12 H: 6 脳 2 = 12 N: 1 脳 2 = 2 O: 1.5 脳 2 = 3
12

Create the empirical formula

颁鈧佲倐贬鈧佲倐狈鈧侽鈧�

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Most popular questions from this chapter

Solutions of sodium carbonate and silver nitrate react to form solid silver carbonate and a solution of sodium nitrate. A solution containing \(3.50 \mathrm{~g}\) of sodium carbonate is mixed with one containing \(5.00 \mathrm{~g}\) of silver nitrate. How many grams of sodium carbonate, silver nitrate, silver carbonate, and sodium nitrate are present after the reaction is complete?

Automotive air bags inflate when sodium azide, \(\mathrm{NaN}_{3}\). rapidly decomposes to its component elements: $$ 2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(\mathrm{s})+3 \mathrm{~N}_{2}(g) $$ (a) How many moles of \(\mathrm{N}_{2}\) are produced by the decomposition of \(1.50 \mathrm{~mol}\) of \(\mathrm{Na} \mathrm{N}_{3}\) ? (b) How many grams of \(\mathrm{NaN}_{3}\) are required to form \(10.0 \mathrm{~g}\) of nitrogen gas? (c) How many grams of \(\mathrm{NaN}_{3}\) are required to produce \(10.0 \mathrm{ft}^{3}\) of nitrogen gas, about the size of an automotive air bag, if the gas has a density of \(1.25 \mathrm{~g} / \mathrm{L} ?\)

Give the empirical formula of each of the following compounds if a sample contains (a) \(0.0130 \mathrm{~mol} \mathrm{C}, 0.0390\) mol \(\mathrm{H}\), and \(0.0065 \mathrm{~mol} \mathrm{O}\); (b) \(11.66 \mathrm{~g}\) iron and \(5.01 \mathrm{~g}\) oxygen; (c) \(40.0 \% \mathrm{C}, 67 \% \mathrm{H}\), and \(53.3 \% \mathrm{O}\) by mass

Detonation of nitroglycerin proceeds as follows: \(4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}(l)\) $$ 12 \mathrm{CO}_{2}(g)+6 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) If a sample containing \(2.00 \mathrm{~mL}\) of nitroglycerin (density \(=1.592 \mathrm{~g} / \mathrm{mL}\) ) is detonated, how many total moles of gas are produced? (b) If each mole of gas occupies \(55 \mathrm{~L}\) under the conditions of the explosion, how many liters of gas are produced? (c) How many grams of \(\mathrm{N}_{2}\) are produced in the detonation?

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 \(=88 \mathrm{~g} / \mathrm{mol}\)
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