In a certain crystalline material the vacancy concentration at 25 c is one-fourth that at 80 c. at what temperature would the vacancy concentration be 3 times that at 80 c?

At 93 °C, the vacancy concentration will be three times that at 80°C.

The formula for the vacancy concentration in a crystal is a form of the Arrhenius equation.

In logarithmic form, the equation is

ln(N_2/N_1) = (-Q/R)(1/T_2-1/T_1)

where

•Q = the energy required for vacancy formation

•N_2 = the vacancy concentration at T_2

•N_1 = the vacancy concentration at T_1

•R = the gas constant [8.314 J·K^(-1)mol^(-1)]

Let N_80 represent the vacancy concentration at 80 °C.

At 25 °C, ln(N_25/N_80) = ln(0.25N_80/N_80) = ln0.25 = -1.386

∴ -1.386 =(-Q/R)(1/298.15 – 1/353.15) = -1.306 × 10^(-4) × (Q/R)

Q/R = (-1.386)/[-1.306 × 10^(-4)] = 10 620

At T_2, ln(N_T2/N_80) = ln[(3N_80)/N_80] = ln3 = 1.099

∴ 1.099 = -10 620(1/T_2 – 1/353.15) = -10 620/T_2 + 10 620/353.15

= -10 620/T_2  + 30.072

10 620/T_2 = 30.072 – 1.099 = 28.97

T_2 = 10 620/28.97 = 366.4 K = 93 °C

answer: the rate of diffusion increases with increase in temperature.

increase in temperature, increases the molecular/particles speed (kinetic energy. diffusion means movement of particles through the material.

generally, the heavier the particle the more it interacts with the environment and more the temperature matters. so higher temperature results in higher diffusion.

your answer would be “dry”