Question

1. which has more atoms: 2.5 mol of calcium carbonate, $\text{caco}_3$, or 3.5 mol of calcium hydroxide, $\text{ca(oh)}_2$?
2. how many grams is 2.50 mol of $\text{h}_2\text{o}$?
3. how many atoms are in 0.750 mol of $\text{na}_3\text{po}_4$?
4. how many moles are present in 20.0 g of $\text{no}_2$?
5. how many formula units are in 171 g of lithium nitride, $\text{li}_3\text{n}$?
6. how many representative particles are in 550.0 g of palladium(iv) oxide, $\text{pdo}_2$?
7. how many formula units are in 0.472 mol of iron(iii) bromide, $\text{febr}_3$?
8. how many fluorine atoms are in 410.0 g of uranium hexafluoride, $\text{uf}_6$?
9. what is the molar volume of a gas?
10. how does the number of particles of nitrogen in a balloon at stp compare to the number of particles of oxygen in a different balloon at stp with the same volume?
11. a compound contains 85.63% carbon and 14.37% hydrogen. what is the empirical formula of the compound?
12. glucose has the formula $\text{c}_6\text{h}_{12}\text{o}_6$. what is the percent composition of each element?
13. how many moles of sodium fluoride are needed to make 500.0 ml of 3.5m solution?
14. how many grams of ethanol, $\text{ch}_3\text{ch}_2\text{oh}$, are needed to make 1.00 l of a 3.50m solution?
15. what is the concentration of each of the following solutions?

a. 3.5 mol $\text{hbr}$ in 500 ml of water
b. 0.0750 mol $\text{nacl}$ in 250.0 ml of water
c. 1.95 mol $\text{agno}_3$ in 1.2 l of water
d. 0.500 mol $\text{nh}_3$ in 2.5 l of water

investigation 6

Explanation:

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Question 16

Step1: Count atoms per formula unit

$\text{CaCO}_3$: $1+1+3=5$ atoms; $\text{Ca(OH)}_2$: $1+2+2=5$ atoms

Step2: Calculate total atoms for each

$2.5\ \text{mol} \times 5 \times 6.022\times10^{23}\ \text{atoms/mol} = 7.5275\times10^{24}\ \text{atoms}$
$3.5\ \text{mol} \times 5 \times 6.022\times10^{23}\ \text{atoms/mol} = 1.05385\times10^{25}\ \text{atoms}$

Step3: Compare the two values

$1.05385\times10^{25} > 7.5275\times10^{24}$

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Question 17

Step1: Find molar mass of $\text{H}_2\text{O}$

$M = (2\times1.008) + 16.00 = 18.016\ \text{g/mol}$

Step2: Calculate mass from moles

$m = n \times M = 2.50\ \text{mol} \times 18.016\ \text{g/mol}$

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Question 18

Step1: Count atoms per formula unit

$\text{Na}_3\text{PO}_4$: $3+1+4=8$ atoms

Step2: Calculate total atoms

$\text{Total atoms} = 0.750\ \text{mol} \times 8 \times 6.022\times10^{23}\ \text{atoms/mol}$

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Question 19

Step1: Find molar mass of $\text{NO}_2$

$M = 14.01 + (2\times16.00) = 46.01\ \text{g/mol}$

Step2: Calculate moles from mass

$n = \frac{m}{M} = \frac{20.0\ \text{g}}{46.01\ \text{g/mol}}$

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Question 20

Step1: Find molar mass of $\text{Li}_3\text{N}$

$M = (3\times6.94) + 14.01 = 34.83\ \text{g/mol}$

Step2: Calculate moles of $\text{Li}_3\text{N}$

$n = \frac{171\ \text{g}}{34.83\ \text{g/mol}}$

Step3: Find formula units

$\text{Formula units} = n \times 6.022\times10^{23}\ \text{units/mol}$

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Question 21

Step1: Find molar mass of $\text{PdO}_2$

$M = 106.42 + (2\times16.00) = 138.42\ \text{g/mol}$

Step2: Calculate moles of $\text{PdO}_2$

$n = \frac{550.0\ \text{g}}{138.42\ \text{g/mol}}$

Step3: Find representative particles

$\text{Particles} = n \times 6.022\times10^{23}\ \text{particles/mol}$

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Question 22

Step1: Relate moles to formula units

$\text{Formula units} = n \times 6.022\times10^{23}\ \text{units/mol}$

Step2: Substitute the given moles

$\text{Formula units} = 0.472\ \text{mol} \times 6.022\times10^{23}\ \text{units/mol}$

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Question 23

Step1: Find molar mass of $\text{UF}_6$

$M = 238.03 + (6\times19.00) = 352.03\ \text{g/mol}$

Step2: Calculate moles of $\text{UF}_6$

$n = \frac{410.0\ \text{g}}{352.03\ \text{g/mol}}$

Step3: Calculate moles of F atoms

$n_{\text{F}} = n \times 6$

Step4: Calculate total F atoms

$\text{F atoms} = n_{\text{F}} \times 6.022\times10^{23}\ \text{atoms/mol}$

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Question 24

Step1: Define molar volume at STP

Molar volume is the volume occupied by 1 mole of a gas at standard temperature and pressure (STP: 1 atm, 273.15 K).

Step2: State the standard value

At STP, 1 mole of any ideal gas occupies 22.4 L.

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Question 25

Step1: Apply Avogadro's Law

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

Step2: Compare the two samples

Both balloons have the same volume at STP, so they have the same number of particles.

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Question 26

Step1: Assume 100g sample, find moles

$n_{\text{C}} = \frac{85.63\ \text{g}}{12.01\ \text{g/mol}} \approx 7.13\ \text{mol}$
$n_{\text{H}} = \frac{14.37\ \text{g}}{1.008\ \text{g/mol}} \approx 14.26\ \text{mol}$

Step2: Find mole ratio

$\frac{n_{\text{H}}}{n_{\text{C}}} = \frac{14.26}{7.13} = 2$

Step3: Write empirical formula

The ratio $\text{C:H} = 1:2$, so empirical formula is $\text{CH}_2$.

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Question 27

Step1: Find molar mass of glucose

$M = (6\times12.01) + (12\times1.008) + (6\times16.00) = 180.156\ \text{g/mol}$

Step2: Calculate % composition of C

$\% \text{C} = \frac{6\times12.01}{180.156} \times 100\%$

Step3: Calculate % composition of H

$\% \text{H} = \frac{12\times1.008}{180.156} \times 100\%$

Step4: Calculate % composition of O

$\% \text{O} = \frac{6\times16.00}{180.156} \times 100\%$

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Question 28

Step1: Convert volume to liters

$V = 500.0\ \text{mL} = 0.5000\ \text{L}$

Step2: Calculate moles from molarity

$n = M \times V = 3.5\ \text{mol/L} \times 0.5000\ \text{L}$

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Question 29

Step1: Find molar mass of ethanol

$M = (2\times12.01) + (6\times1.008) + 16.00 = 46.068\ \text{g/mol}$

Step2: Calculate moles of ethanol

$n = M_{\text{soln}} \times V = 3.50\ \text{mol/L} \times 1.00\ \text{L}$

Step3: Calculate mass of ethanol

$m = n \times M = 3.50\ \text{mol} \times 46.068\ \text{g/mol}$

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Question 30

Step1: Convert volumes to liters

a. $V = 500\ \text{mL} = 0.500\ \text{L}$; b. $V = 250.0\ \text{mL} = 0.2500\ \text{L}$; c. $V = 1.2\ \text{L}$; d. $V = 2.5\ \text{L}$

Step2: Calculate molarity for each

a. $M = \frac{3.5\ \text{mol}}{0.500\ \text{L}}$
b. $M = \frac{0.0750\ \text{mol}}{0.2500\ \text{L}}$
c. $M = \frac{1.95\ \text{mol}}{1.2\ \text{L}}$
d. $M = \frac{0.500\ \text{mol}}{2.5\ \text{L}}$

Answer:

1. 3.5 mol of calcium hydroxide ($\text{Ca(OH)}_2$) has more atoms.
2. $45.0\ \text{g}$
3. $3.61\times10^{24}\ \text{atoms}$
4. $0.435\ \text{mol}$
5. $2.96\times10^{24}\ \text{formula units}$
6. $2.40\times10^{24}\ \text{representative particles}$
7. $2.84\times10^{23}\ \text{formula units}$
8. $4.30\times10^{24}\ \text{fluorine atoms}$
9. At standard temperature and pressure (STP, 1 atm and 273.15 K), the molar volume of any ideal gas is 22.4 liters per mole.
10. The number of nitrogen particles is equal to the number of oxygen particles.
11. $\text{CH}_2$
12. $\% \text{C} = 40.00\%$, $\% \text{H} = 6.71\%$, $\% \text{O} = 53.29\%$
13. $1.8\ \text{mol}$
14. $161\ \text{g}$
15. a. $7.0\ \text{M}$; b. $0.300\ \text{M}$; c. $1.6\ \text{M}$; d. $0.20\ \text{M}$