When 5.6g of solid KOH was added to 100gof water, the solid completely dissolves. This was accompanied by a rise of 13℃in the water temperature. Calculate the heat of solution of KOH in kJ/mol of KOH

= 57.7kJ/mol

Explanation:

The heat of dissolution is the heat produced when all KOH is dissolved:

KOH(aq) → K⁺(aq) + OH⁻(aq)

To find the heat of solution that is the heat released per mole of KOH we need to convert the mass of KOH to moles and using the equation:

Q = -m×C×ΔT

- Q = Heat; m the mass of solution; C specific heat (We can use specific heat of water 4.184J/g°C), and ΔT change in temperature-

To solve the heat released we can find the heat of solution

Moles KOH -Molar mass: 56g/mol-:

5.6g KOH * (1mol /56g) = 0.1 moles KOH

Heat released:

Q = -106g* 4.184J/g°C* 13°C

Q = -5766J = -5.77kJ

Heat of solution:

5.77kJ / 0.1mol

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