Which formula can be used to calculate the theoretical yield? which formula can be used to calculate the theoretical yield?

step 1

determine the number of moles of each reactant. for solids, divide the mass of a reactant used by its molecular weight. for liquids and gases, multiply the volume by the density and then divide by the molecular weight.

step 2

multiply the molecular weight by the number of moles in the equation. the reactant that has the smallest mole number is the limiting reagent.

step 3

calculate the theoretical mole yield by using the chemical equation. the multiply the ratio between the limiting reagent and the product by the number of moles of the limiting reagent used in the experiment. for example, if your equation was 4al + 3o2 yields 2 al2o3, and al was your limiting reagent, you would divide the number of al moles used by two because it takes four moles of al to make two moles of al2o3, a ratio of two to one.

step 4

multiply the number of moles of the product by the molecular weight of the product to determine the theoretical yield. for example, if you created 0.5 moles of al2o3, the molecular weight of al2co3 is 101.96 g/mol, so you would get 50.98 grams as the theoretical yield.

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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

answer; natural resources;