What is visual reaction time?

I'm so confused :( What is the rate constant when given pressure and time for a 1st order reaction?

• What is the rate constant when given pressure and time for a 1st order reaction? How would I do this? Here is the question: The following gas-phase reaction was studied at 290°C by observing the change in pressure as a function of time in a constant-volume vessel. ClCO2CCl3 (g) → 2COCl2 (g) Time (s)___P (mmHg) 0________15.76 181______18.88 513______22.79 1164_____27.08 Where P is the total pressure From the data, I was able to find out that it was a 1st order reaction when I graphed it. I'm just having trouble finding the rate constant (which should be 1.08x10^-3 s^-1)

• Answer:

  When reaction problems like this involve pressure they can be a little confusing. The first thing you have to do is determine the partial pressure of the gas COCl2. Since 2 moles COCl2 are made for every one mole ClCO2CCl3, you can represent the partial pressure of COCl2 as: P(COCl2) = P(o) Total - (P Total - P(o) Total) Where P(o) Total is the original total pressure, and P Total is the total pressure at each given time. Using that formula you get the following partial pressure values: 15.76 @ 0 sec 12.64 @ 181 sec 8.73 @ 573 sec 4.44 @ 1164 sec You plot the natural log of these values against time and the slope will equal -k, so just take the negative sign off to find the rate constant of 1.08*10^-3 s^-1 Now you could also use the integrated first order rate law to solve for k without graphing: ln Pt = -k(t) + ln Po Where Pt is partial pressure at time t, t is time, and Po is initial partial pressure. Rearrange: (ln(Pt/Po))/t = -k ln (4.44/15.76) / 1164 = -k k= 1.08*10^3 s^-1 Hope that helps you out.