What is the heat of a reaction, in joules, with a total reaction mixture volume of 62.3 mL of the reaction causes a temperature change of 5.0 oC in a calorimeter

1,303.316 J = 1.303316 KJ.

Explanation:

The first thing to do is to calculate or Determine the mass. Thus, from the question/problem above some basic parameters or data or information were provided which is going to aid in solving this particular Question;

=> total reaction mixture volume =62.3 mL and the reaction temperature change = of 5.0 oC

The mass = density × total reaction mixture volume = 1 × 62.3 = 62.3 grams.

Therefore, the heat of a reaction = mass × specific heat capacity (C) × temperature change (∆T).

Thus, the heat of reaction = 62.3 grams × 4.184 J/g-°C × 5.0°C = 1,303.316 J = 1.303316 KJ.

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