1. Answer the following questions about magnesium. — Atomic Structure, Mass Spectrometry, Ion-Dipole Interactions, Solubility Equilibria Chemistry Question
Problem Context
- Answer the following questions about magnesium.
A. An incomplete mass spectrum for magnesium is shown in the diagram.
The percent abundance of magnesium-24 is 79%. The percent abundances of the other two natural isotopes of magnesium, magnesium-25 and magnesium-26, are approximately equal.
i. Complete the mass spectrum in part A by drawing thick lines in the appropriate locations to represent the percent abundance of magnesium-25 and magnesium-26.
Model Answer
The abundance for the two lines should be between 10 and 11 [1].
ii. Describe the difference in atomic structure that accounts for the difference in mass between magnesium-25 and magnesium-26.
Model Answer
Magnesium-26 has one more neutron than magnesium-25 does [1, 2].
A student prepares a 1.85 × 10^-3 M solution of Mg(NO3)2(aq) in beaker 1 and a 2.80 × 10^-4 M solution of NaOH(aq) in beaker 2, as shown.
B. The particle diagram shown represents a magnesium ion, Mg2+, in beaker 1. A sodium ion, Na+, in beaker 2 has a weaker attraction to water than the Mg2+ does. Explain this phenomenon using Coulomb’s law and each of the following.
i. The relative charge of the ions
Model Answer
The charge on the sodium ion is less than the charge on the
magnesium ion [2]. A smaller charge results in a weaker Coulombic attraction
between Na⁺ and water [2].
ii. The relative radii of the ions
Model Answer
The Na⁺ ion is larger than the Mg²⁺ ion, so the distance between
the Na⁺ and the oxygen on the water molecule will be greater [2]. As distance
increases, Coulombic attraction decreases [2].
C. Calculate the pH of the solution in beaker 2.
Model Answer
pOH = −log(2.80 × 10⁻⁴) = 3.553 [2, 3]
pH = 14 − pOH = 14 − 3.553 = 10.447 [3]
D. A student combines 35.00 mL of 1.85 × 10^-3 M Mg(NO3)2(aq) with 50.00 mL of 2.80 × 10^-4 M NaOH(aq), as shown in the diagram. Calculate [Mg2+] after the two solutions are combined but before any reaction takes place. (Assume that volumes are additive.)
Model Answer
M₁V₁ = M₂V₂ [3]
M₂ = (1.85 × 10⁻³ M)(0.03500 L) / (0.03500 L + 0.05000 L) = 7.62 × 10⁻⁴ M [3]
E. The dissolution of magnesium hydroxide is represented by the following equation.
Mg(OH)2(s) ⇌ Mg2+(aq) + 2 OH-(aq) Ksp = 5.61 × 10^-12
i. Write the expression for the solubility product constant, Ksp.
Model Answer
Kₛₚ = [Mg²⁺][OH⁻]² [3]
ii. After the two solutions are combined in beaker 3 as described in part D, but before any reaction takes place, [OH-] = 1.65 × 10^-4 M. Using your answer to part D, calculate the value of the reaction quotient, Q.
Model Answer
Q = [Mg²⁺][OH⁻]² = (7.62 × 10⁻⁴)(1.65 × 10⁻⁴)² = 2.07 × 10⁻¹¹
[3]
iii. Using the reaction quotient, Q, predict whether a precipitate should form as the mixture in beaker 3 approaches equilibrium. Justify your answer.
Model Answer
Examples of acceptable responses may include the following:
* Q > Kₛₚ, so a precipitate will form [3, 4].
* The concentration of the ions in solution (represented by Q) is greater than
that of a saturated solution, so a precipitate will form [4].
F. In a separate experiment, the student adds HNO3(aq) to decrease the pH of a saturated solution containing undissolved Mg(OH)2(s). Does the amount of undissolved Mg(OH)2(s) increase, decrease, or remain the same as the HNO3(aq) is added? Justify your answer.
Model Answer
Decrease [4]. The H⁺ from HNO₃(aq) will react with OH⁻, decreasing
[OH⁻] and causing Q < Kₛₚ [4]. As a result, more Mg(OH)₂(s) will dissolve until
equilibrium is reestablished, resulting in less Mg(OH)₂(s) [4].
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