For the hypothetical reaction a+3b2c, the rate of appearance of c given by

a) (δ[c]/δt = -δ[a]/δt
b) (δ[c]/δt = -(3/2)δ[b]/δt
c) (δ[c]/δt = -(2/3)δ[b]/δt
d) (δ[c]/δt = -(1/2)δ[a]/δt

Δ[C]/Δt = (-2/3)*Δ[B]/Δt

thus the answer C is correct

Explanation:

Assuming that the reaction is

A+3B→2C

then denoting C as the concentrations and ν as the stoichiometric coefficients

(Ca-Ca₀)/νa = (Cb-Cb₀)/νb = (Cc-Cc₀)/νc

differenciating with respect to t

(dCa/dt)/νa = (dCb/dt)/νb = (dCc/dt)/νc

then

dCc/dt = (νc/νa)*(dCa/dt)

dCc/dt = (νb/νa)*(dCb/dt)

since νa=1 , νb=3 , νc=(-2) , doing Δ[C]/Δt= dCc/dt and for the other components

Δ[C]/Δt = (-2)*Δ[A]/Δt

Δ[C]/Δt = (-2/3)*Δ[B]/Δt

thus the answer C is correct

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