Chemical Reaction Engineering homework

[herbertpbarreto]

Homework Statement

The decomposition of phosphine 4PH3(g) + P4(g) + 6H2(g) is first-order with respect to phosphine with a rate constant k = 0.0155 s-l at 953 K. If the decomposition occurs in a constant-volume batch reactor at 953 K, calculate, for 40% conversion of PH3,

(a) the time required, s;
(b) the mole fraction of H2 in the reaction mixture.

Homework Equations

(
-rA)=-dCa/dT
(-rA)=kCa
Ca= Ca0 (1-Xa)

The Attempt at a Solution

a) i attempet do apply the equation for spatial time I am batch reactors:
-dCa/dT = kCa
∫-dCa/Ca =∫kdT
-ln(Ca/Ca0) = kT
-ln (Ca0(1-Xa)/Ca0) = kT
-ln (1-Xa) = kT --> -ln (1-0,4) = 0,0155 * T --> -ln(0,6)/0,0155 =T
T = 32,96 s
b) i have no idea

 

[epenguin]

Homework Statement

The decomposition of phosphine 4PH3(g) + P4(g) + 6H2(g) is first-order with respect to phosphine with a rate constant k = 0.0155 s-l at 953 K. If the decomposition occurs in a constant-volume batch reactor at 953 K, calculate, for 40% conversion of PH3,

(a) the time required, s;
(b) the mole fraction of H2 in the reaction mixture.

b) i have no idea

So of the total original molecules of PH₃ 0.6 of them are still PH₃, and of the 0.4 that have reacted each one has become 1.5 molecules of H₂ and ¼ of P₄ according to your formula (which should have a → instead of a + ) and you have any difficulty in finding what fraction H₂ molecules are of the total?