Question

Determine whether the statements given below are true or false. (a) The mass of an atom can have the unit mole. (b) In \(\mathrm{N}_{2} \mathrm{O}_{4},\) the mass of the oxygen is twice that of the nitrogen. (c) One mole of chlorine atoms has a mass of \(35.45 \mathrm{~g}\). (d) Boron has an average atomic mass of 10.81 amu. It has two isotopes, \(\begin{array}{lll}\text { B-10 } & (10.01 \text { amu }) & \text { and } & \text { B-11 }\end{array}\) (11.01 amu). There is more naturally occurring B-10 than B-11. (e) The compound \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{2} \mathrm{~N}\) has for its simplest formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O} \mathrm{N}_{1 / 2}\) (f) A 558.5 -g sample of iron contains ten times as many atoms as \(0.5200 \mathrm{~g}\) of chromium. (g) If \(1.00 \mathrm{~mol}\) of ammonia is mixed with \(1.00 \mathrm{~mol}\) of oxygen the following reaction occurs, \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) All the oxygen is consumed. (h) When balancing an equation, the total number of moles of reactant molecules must equal the total number of moles of product molecules.

Short answer

Question: Determine whether each of the following statements is true or false. a) The mass of an atom can have the unit mole. b) The mass of oxygen is twice that of nitrogen in N2O4. c) One mole of chlorine atoms has a mass of 35.45 g. d) There is more naturally occurring B-10 than B-11 when boron has an average atomic mass of 10.81 amu. e) The simplest formula of C6H12O2N is C3H6ON(1/2). f) A 558.5-g sample of iron contains ten times as many atoms as 0.5200 g of chromium. g) All the oxygen is consumed when 1.00 mol of ammonia is mixed with 1.00 mol of oxygen and the given reaction occurs. h) The total number of moles of reactant molecules must equal the total number of moles of product molecules when balancing an equation. Answer: a) False b) False c) True d) False e) False f) True g) False h) False

Step-by-step solution

(a) Determine if the mass of an atom can have the unit mole.

To answer this question, let us recall that the mole is a unit of measurement for the amount of a substance. It is not a unit of mass. Therefore, this statement is false.

(b) Determine if the mass of oxygen is twice that of nitrogen in N2O4.

To calculate the mass ratio of oxygen to nitrogen in N2O4, we can use the atomic masses of nitrogen and oxygen. The atomic mass of nitrogen is 14.01 amu, and the atomic mass of oxygen is 16.00 amu. There are two nitrogen atoms and four oxygen atoms in the molecule. Therefore, the total mass of nitrogen is 2 * 14.01 = 28.02 amu. The total mass of oxygen is 4 * 16.00 = 64.00 amu. The ratio of the oxygen mass to nitrogen mass is 64.00 / 28.02 ≈ 2.28, which is not exactly twice. Therefore, this statement is false.

(c) Determine if one mole of chlorine atoms has a mass of 35.45 g.

The atomic mass of chlorine is approximately 35.45 amu. By definition, one mole of a substance contains Avogadro's number of entities (atoms, ions, or molecules), and the molar mass in grams is numerically equal to the atomic mass in amu. Therefore, one mole of chlorine atoms has a mass of approximately 35.45 g. Thus, this statement is true.

(d) Determine if there is more naturally occurring B-10 than B-11 when boron has an average atomic mass of 10.81 amu.

To verify this statement, we need to compare the isotopic abundance of B-10 and B-11. The average atomic mass of boron is given as 10.81 amu, considering the masses and relative abundance of both isotopes. If the average atomic mass is closer to 11.01 amu (the mass of B-11), then B-11 should be more abundant. Since 10.81 amu is closer to 11.01 amu than 10.01 amu, it is more likely that B-11 is more abundant than B-10. Therefore, this statement is false.

(e) Determine if the simplest formula of C6H12O2N is C3H6ON(1/2).

This statement suggests that dividing the compound's subscripts by a common factor will give a whole-number ratio for the elements. However, dividing the subscripts of C6H12O2N by 2 results in C3H6O1N(1/2), which is not a whole-number ratio because of the fractional nitrogen value. Therefore, this statement is false.

(f) Determine if a 558.5-g sample of iron contains ten times as many atoms as 0.5200 g of chromium.

To verify this statement, we need to calculate the number of moles of iron and chromium, and then compare their ratios. The molar mass of iron is 55.85 g/mol, and the molar mass of chromium is 51.996 g/mol. The number of moles of iron in a 558.5-g sample is (558.5 g) / (55.85 g/mol) ≈ 10 moles. The number of moles of chromium in a 0.5200-g sample is (0.5200 g) / (51.996 g/mol) ≈ 0.01 moles. Since the number of moles of iron (10 moles) is ten times the number of moles of chromium (0.01 moles), this statement is true.

(g) Determine if all the oxygen is consumed when 1.00 mol of ammonia is mixed with 1.00 mol of oxygen and the given reaction occurs.

To verify this statement, let's look at the stoichiometry of the given reaction: 4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(l). According to the balanced equation, 4 moles of ammonia react with 5 moles of oxygen. Therefore, if we have 1 mole of ammonia and 1 mole of oxygen, the reaction will not consume all of the 1 mole of oxygen, as it requires a 4:5 ratio. Thus, this statement is false.

(h) Determine if the total number of moles of reactant molecules must equal the total number of moles of product molecules when balancing an equation.

When balancing a chemical equation, the goal is to ensure that the number of atoms of each element is conserved, i.e., the same on both sides of the equation. This conservation of atoms does not necessarily require that the total number of moles of reactants equal the total number of moles of products, as different molecules may have different numbers of atoms. Thus, this statement is false.