The formula for a lutetium carbonate compound is Lu2(CO3)3. What would be the formula for a lutetium nitrate compound given that the charge of lutetium is the same in both compounds? a. LuNO3
b. Lu2NO3
c. Lu(NO3)2
d. Lu2(NO3)3
e. Lu(NO3)3

E

Explanation:

From Lu2(CO3)3, we can determine the charge of the variable charge transition metal Lu has a charge of 3, as CO3 has a 2- charge (3*-2 = 6, 6/2 = 3). Then, we apply this to nitrate, which has a charge of 1-. Balance charges, reduce, and you get E.

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

c- cold periods in earth's history during which glaciers covered much of the surface.

explanation: