Question

Box A contains 36 atoms of arsenic (As) and 27 molecules of \(\mathrm{O}_{2} .\) Box \(\mathrm{B}\) contains 18 molecules of \(\mathrm{As}_{2} \mathrm{O}_{3} .\) Without using your calculator, compare Box A to Box B with respect to (a) the number of atoms of arsenic and oxygen. (b) the number of discrete particles. (c) mass.

Short answer

Question: Compare Box A containing 36 atoms of arsenic and 27 molecules of oxygen to Box B containing 18 molecules of arsenic trioxide (As2O3) in terms of their number of atoms of arsenic and oxygen, number of discrete particles, and mass. Answer: Box A and Box B have an equal number of arsenic atoms (36) and oxygen atoms (54). However, Box A has more discrete particles (63) compared to Box B (18). Despite the difference in the number of discrete particles, the mass of both boxes is the same at 3557.12 u.

Step-by-step solution

Analyze the content of each box

In Box A, there are 36 atoms of arsenic and 27 molecules of oxygen. In Box B, there are 18 molecules of arsenic trioxide (As2O3).

Break down the content of Box B

Each molecule of As2O3 contains 2 arsenic atoms and 3 oxygen atoms. So, in 18 molecules of As2O3, there will be 18 * 2 arsenic atoms and 18 * 3 oxygen atoms.

Compare the number of atoms

In Box A, there are 36 arsenic atoms. In Box B, there are 18 * 2 = 36 arsenic atoms. Hence, Box A and Box B have equal number of arsenic atoms. In Box A, there are 27 oxygen molecules, and each molecule has 2 oxygen atoms. So, there are 27 * 2 = 54 oxygen atoms in Box A. In Box B, there are 18 * 3 = 54 oxygen atoms. Therefore, Box A and Box B have equal number of oxygen atoms as well. #b) Number of discrete particles.#

Identify discrete particles in each box

In Box A, there are 36 atoms of arsenic and 27 molecules of oxygen. In Box B, there are 18 molecules of As2O3.

Compare the number of particles

Box A has a total of 36 + 27 = 63 discrete particles. Box B has a total of 18 discrete particles. Hence, Box A has more discrete particles compared to Box B. #c) Mass.#

Calculate the mass of the contents of Box A

Box A contains 36 arsenic atoms and 27 oxygen molecules. So, the mass of Box A would be 36 * (74.92 u) + 27 * (2 * 16.00 u) = 2693.12 u + 864.00 u = 3557.12 u.

Calculate the mass of the contents of Box B

Box B contains 18 molecules of As2O3. The molar mass of As2O3 is (2 * 74.92 u) + (3 * 16.00 u) = 149.84 u + 48.00 u = 197.84 u. So, the mass of Box B would be 18 * 197.84 u = 3557.12 u.

Compare the masses of the boxes

Both Box A and Box B have a mass of 3557.12 u. Hence, Box A and Box B have the same mass.