Consider the equilibrium c2h6(g) ↔ c2h4(g) + h2(g) . at 1000k and a constant total pressure of 1 bar, h2(g) is introduced into the reaction vessel. the total pressure is held constant at 1 bar and at equilibrium the composition of the mixture in mole percent is h2 : 26% ; c2h4: 26% ; c2h6 : 48%calclate kp at 1000 k.

Explanation:

From the reaction:

C₂H₆(g) ⇆ C₂H₄(g) + H₂(g)  

 48%          26%       26%

Knowing the composition of the mixture at equilibrium (at 1000K), we can calculate the equilibrium constant in terms of mole fraction:          

where X: mole fraction of C₂H₆(g), C₂H₄(g) and H₂(g)  

Now, the equilibrium constant in terms of pressure can be calculated using the equilibrium constant in terms of mole fraction:      

where : total pressure and Δn: number of gaseous moles of product - number of gaseous moles of reactant  

Have a nice day!

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

the answer is minerals.