PRE-LAB ASSIGNMENT: Practice Calculations
Use the data provided to complete the following calculations in your lab notebook:
DATAI:
Mass of empty crucible
22.498
Mass of crucible + hydrate 26.70 g
(before heating)
Mass of crucible + anhydrous salt 25.82 g
(after first heating)
Mass of crucible + anhydrous salt 25.81 g
(after second heating)
a. Determine the mass of hydrate used.
Mass of hydrate - (Mass of crucible + hydrate before heating) - (Mass of empty crucible)
b. Determine the mass of anhydrous salt.
Mass of anhydrous salt - (Mass of crucible + anhydrous salt after final heating) - (Mass of empty
crucible)
c. Determine the mass of water.
Mass of water - (Mass of hydrate)- (Mass of anhydrous salt)
d. Determine the percentage of water in the hydrate.
% water - Mass of water x 100
Mass of hydrate

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

> b takes place in the gas phase in an isothermal tubular reactor. the feed is one mole of a per one mole of c, an inert. the entering temperature and pressure are 427°c and 10 atm, respectively. the gas constant r = 0.08206 atm · l/mol · k.