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, \(\mathrm{B}-10(10.01\) amu \()\) and \(\mathrm{B}-11(11.01 \mathrm{amu}) .\) 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 \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{ON}_{1 / 2}\). (f) A 558.5-g sample of iron contains ten times as many atoms as \(0.5200 \mathrm{~g}\) of chromium. (g) If \(1.00\) mol of ammonia is mixed with \(1.00\) 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# True or False: In \(\mathrm{N}_{2} \mathrm{O}_{4}\), the mass of the oxygen is twice that of the nitrogen.

Step-by-step solution

Answer

False. The mass of an atom is typically measured in atomic mass units (amu), not in moles. A mole is a unit of measurement used for counting entities like atoms or molecules. #b) True or False: In \(\mathrm{N}_{2} \mathrm{O}_{4}\), the mass of the oxygen is twice that of the nitrogen.#

Answer

True. In \(\mathrm{N}_{2} \mathrm{O}_{4}\), there are 2 nitrogen atoms and 4 oxygen atoms. Since the molar mass of nitrogen is approximately 14 g/mol and the molar mass of oxygen is approximately 16 g/mol, the mass of oxygen in the molecule is indeed twice the mass of nitrogen: \((2 \times 14) = (4\times 16)\) #c) True or False: One mole of chlorine atoms has a mass of \(35.45 \mathrm{~g}\).#

Answer

True. The atomic mass of chlorine is approximately 35.45 amu. Therefore, one mole of chlorine atoms would have a mass of 35.45 g/mol. #d) True or False: There is more naturally occurring B-10 than B-11.#

Answer

False. Boron has an average atomic mass of 10.81 amu, which is closer to the atomic mass of B-11 (11.01 amu) than to the atomic mass of B-10 (10.01 amu). This indicates that there is a higher abundance of B-11 isotopes compared to B-10 isotopes. #e) True or False: The compound \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{2} \mathrm{~N}\) has for its simplest formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{ON}_{1 / 2}\).#

Answer

False. A simplest formula should not have fractional values for the subscripts. The simplest formula for the given compound is \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{2} \mathrm{N}\). #f) True or False: A 558.5-g sample of iron contains ten times as many atoms as \(0.5200 \mathrm{~g}\) of chromium.#

Answer

True. To compare the number of atoms in both samples, we have to convert grams to moles. Using the molar mass of iron (55.85 g/mol) and chromium (51.996 g/mol): Moles of iron = \(\frac{558.5 \, \text{g}}{55.85 \, \text{g/mol}} \approx 10 \, \text{moles}\) Moles of chromium = \(\frac{0.5200\, \text{g}}{51.996 \, \text{g/mol}} \approx 0.01 \, \text{moles}\) Ten times the moles of chromium is equal to the moles of iron, indicating they contain the same number of atoms. #g) True or False: All the oxygen is consumed in the reaction.#

Answer

True. The reaction is balanced and shows that 5 moles of oxygen react with 4 moles of ammonia. If 1 mole of each reactant is mixed, the oxygen will be consumed completely since the ratio of moles of reactants matches the stoichiometry of the balanced equation. #h) True or False: When balancing an equation, the total number of moles of reactant molecules must equal the total number of moles of product molecules.#

Answer

False. When balancing an equation, it is the total number of atoms for each element that must be equal on both sides of the reaction, not the moles of the reactants and products.

Key concepts

Molar Mass

Molar mass is an essential concept in chemistry, as it helps us determine the amount of substance in a given number of molecules or atoms. It refers to the mass of one mole of a substance, commonly expressed in grams per mole (g/mol). One mole of any element or compound contains Avogadro's number of particles, approximately \( 6.022 \times 10^{23} \) entities. This concept allows chemists to conveniently convert between grams of a substance and its corresponding number of moles.

To illustrate, consider chlorine: its atomic mass is around 35.45 amu, making the molar mass 35.45 g/mol. This means that 35.45 grams of chlorine would contain one mole, or \( 6.022 \times 10^{23} \), chlorine atoms. Understanding molar mass is crucial for calculations involving chemical reactions and conversions between mass and moles.

• Molar mass links atomic mass to larger amounts, like grams or kilograms.
• Helps in converting mass of substances to moles—an essential step in stoichiometry.

Stoichiometry

Stoichiometry is a fundamental part of chemistry that involves using relationships between reactants and products in a chemical reaction to determine desired quantitative data. It is based on the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. In simple terms, stoichiometry allows us to predict how much reactant is needed to produce a certain amount of product.

To perform stoichiometric calculations, one must start with a balanced chemical equation. This provides the mole ratio of reactants to products, which is key for calculating the quantities of substances involved in the reaction. For example, in the reaction \( 4 \text{NH}_3(g) + 5 \text{O}_2(g) \rightarrow 4 \text{NO}(g) + 6 \text{H}_2\text{O}(l) \), the coefficients indicate the ratio of moles needed: 4 moles of \( \text{NH}_3 \) react with 5 moles of \( \text{O}_2 \) to produce 4 moles of \( \text{NO} \) and 6 moles of \( \text{H}_2\text{O} \). If only 1 mole of each reactant is used, the oxygen will be consumed as soon as the stoichiometric balance is achieved.

• Stoichiometry uses balanced equations to calculate reactant and product quantities.
• It involves mole ratios based on the coefficients from the balanced equation.

Atomic Mass

Atomic mass is the average mass of an atom of an element, measured in atomic mass units (amu). It provides insight into the mass of individual atoms on a relative scale, primarily considering the protons and neutrons within the nucleus. Electrons are also present, but their mass is negligible compared to protons and neutrons.

Since most elements exist as a variety of isotopes, the atomic mass represents an average of all natural isotopic forms, weighted by their relative abundance. For instance, the atomic mass of boron is roughly 10.81 amu, suggesting a mix of its isotopes B-10 and B-11, with the latter being more abundant.

• Atomic mass is a weighted average of all isotopes of an element.
• Expressed in atomic mass units (amu), reflecting the mass of protons and neutrons.

Isotopes

Isotopes are different forms of the same element that have the same number of protons but a different number of neutrons in their nuclei. This means they have identical atomic numbers but different mass numbers. Isotopes can occur naturally or can be synthetically produced.

A classic example is carbon, which has isotopes like Carbon-12 and Carbon-14. These isotopes form due to variations in the number of neutrons but maintain the same chemical properties because they have the same number of electrons. Their differing mass numbers, however, affect their average atomic mass and sometimes their nuclear stability.

• Isotopes have the same chemical properties but differ in nuclear properties.
• Can lead to differences in average atomic masses for elements.