What is the molar solubility of MgF2 in a 0.36 M Mg(NO3)2 solution? For MgF2, Ksp = 8.4 × 10^–8

2.4 × 10⁻⁴ M

Explanation:

Step 1: Calculate the concentration of Mg²⁺ coming from Mg(NO₃)₂

Mg(NO₃)₂ is a strong electrolyte and the molar ratio of Mg(NO₃)₂ to Mg²⁺ is 1:1. The initial molar concentration of Mg²⁺ is 1/1 × 0.36 M = 0.36 M.

Step 2: Make an ICE chart for the solution of MgF₂

        MgF₂(s) ⇄ Mg²⁺(aq) + 2 F⁻(aq)

I                           0.36             0

C                           +S             +2S

E                         0.36+S         2S

The solubility product constant is:

Ksp = [Mg²⁺] × [F⁻]² = (0.36+S) × (2S)²

Since S <<< 0.36, 0.36+S ≈ 0.36.

Ksp = 0.36 × 4S² = 8.4 × 10⁻⁸

S = 2.4 × 10⁻⁴ M

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

smooth muscle is composed of involuntary muscles found within the walls of organs and structures such as the esophagus, stomach, intestines, and blood vessels. those muscles push materials like food or blood through organs. unlike skeletal muscle, smooth muscle can never be under your control.