# Chemistry and Derivatives!

• Feb 9th 2010, 04:42 PM
stellarmathstudent
Chemistry and Derivatives!
I have a calculus project due tomorrow and help would be greatly appreciated!
The problem: Imagine that .00158 moles of CO2 is contained in a closed pipette whose volume is decreasing at the rate of .001L/sec, while the pressure is increasing at the rate of 1/2 atm/sec and the moles are increasing at a rate of .0001881moles/sec. How fast is temperature changing when pressure is 5.2atm, volume is .0055L Moles increase at a rate of .0001881 moles per second.

The equation we wish to take the derivative of is PV=nRT, solving for the rate of change of temperature over time. (dT/dt).

To make it more clear:
dP/dt= .5atm/sec P=5.2 atm
dV/dt= -.001 L/sec V= .0055L
dT/dt=? T= 220 K
dn/dt=.0001881 n=.00158
R=.08206

Thanks in advance, I have tried to solve this problem for the past week and cannot get a reasonable answer for dT/dt.
• Feb 9th 2010, 05:46 PM
blackcompe
I solved the ideal gas law for T: T = PV/nR. Therefore, T', which is the rate of change of the temperature with respect to time is: ((PV)'(nR) - (PV)(nR)') / (nR)^2, by way of the product rule.

T' = ((PV)'(nR) - (PV)(nR)') / (nR)^2
= ((P'V + PV')(nR) - (PV)(n'R + nR')) / (nR)^2

Since you've got P', V', n', and you know derivative of a constant, R, is 0, you can solve for T'. I got approximately -45 K/sec for T'. Good luck.