Question

part ii: multiple choice: merely circling the answers does not mean youve learned anything. the goal is to reinforce the material. justify your answer, either by showing work for a calculation or writing a short explanation. “give an honest effort now. enjoy your success in the future”. 1. which of the following numerical expressions gives the number of moles in 5.0 g of cao? a. 5.0g × 56 g/mol c. $\frac{56 g/mol}{5.0g}$ b. $\frac{5.0 g}{56.0 g/mol}$ d. 15.0 g × 56 g/mol 2 in a lab a student is given a 21g sample of pure cu metal. which of the following pieces of information is most useful for determining the number of cu atoms in the sample? assume that the pressure and temperature in the lab are 1.0atm and 25°c. a. the molar mass of cu b. the density of cu at 25°c c. the volume of the cu sample d. the ratio of the two main isotopes found in pure cu 3. a 1.0 mol sample of which of the following compounds has the greatest mass? a. no b. no₂ c. n₂o d. n₂o₅ 4 the mass spectrum for an unknown element is shown to the right. according to the information in the spectrum, the atomic mass of the unknown element is closest to a. 90 amu b. 91 amu c. 93 amu d. 94 amu

Explanation:

Step1: Recall mole - mass formula

The formula to calculate the number of moles $n$ is $n=\frac{m}{M}$, where $m$ is the mass and $M$ is the molar mass. For $CaO$, the molar mass $M$ of $CaO$ is approximately $40 + 16=56\ g/mol$, and $m = 5.0\ g$. So the number of moles of $CaO$ is $n=\frac{5.0\ g}{56\ g/mol}$, so the answer to question 1 is B.

Step2: Determine useful info for atom - number calculation

To find the number of atoms of $Cu$, first we need to find the number of moles of $Cu$ using $n=\frac{m}{M}$, where $m$ is the mass of the $Cu$ sample and $M$ is the molar mass of $Cu$. Then we use Avogadro's number $N = n\times N_A$. The molar mass of $Cu$ is most useful for determining the number of moles and then the number of atoms. So the answer to question 2 is A.

Step3: Calculate molar masses of compounds

The molar mass of $NO$: $M_{NO}=14 + 16=30\ g/mol$. The molar mass of $NO_2$: $M_{NO_2}=14+2\times16 = 46\ g/mol$. The molar mass of $N_2O$: $M_{N_2O}=2\times14 + 16=44\ g/mol$. The molar mass of $N_2O_5$: $M_{N_2O_5}=2\times14+5\times16 = 108\ g/mol$. For a 1.0 - mol sample, mass $m=n\times M$, so the compound with the greatest mass is $N_2O_5$. The answer to question 3 is D.

Step4: Calculate atomic mass from mass - spectrum

Let's assume the abundances of the isotopes at atomic masses 90, 92, 94, 96 are $a_1$, $a_2$, $a_3$, $a_4$ respectively. From the graph, assume $a_1\approx100$, $a_2\approx20$, $a_3\approx20$, $a_4\approx5$ (relative abundances). The atomic mass $A$ is calculated as $A=\sum_{i}M_i\times a_i/\sum_{i}a_i$. $A=\frac{90\times100 + 92\times20+94\times20 + 96\times5}{100 + 20+20 + 5}=\frac{9000+1840 + 1880+480}{145}=\frac{13200}{145}\approx91\ amu$. The answer to question 4 is B.

Answer:

1. B. $\frac{5.0\ g}{56.0\ g/mol}$
2. A. The molar mass of $Cu$
3. D. $N_2O_5$
4. B. 91 amu