The temperature of the mixture starts at 97.5 Celsius and changes by -7.5 Celsius every 3.5 min for 35 minutes. Then the temperature changes more slowly, by -3.

Question

a chemist is cooling a reaction mixture with an ice and salt bath. The temperature of the mixture starts at 97.5 Celsius and changes by -7.5 Celsius every 3.5 min for 35 minutes. Then the temperature changes more slowly, by -3.5 Celsius every 7.5 minutes. How long does the mixture stay in the ice and salt bath to reach a temperature of 5 Celsius?

Answer 1

starts at 97.5 Celsius

 

changes by -7.5 Celsius every 3.5 min for 35 minutes.  (-7.5 C/ 3.5 min ) x 35 min = -70.5 C

 

So, now we are at 97.5 - 70.5 = 27.0 C

 

Want to get to 5 C.  So, 27.0 - 5 = 22 degrees to go (lower)

 

(3.5 degrees/ 7.5 minutes)(x minutes)  = 22 degrees

 

x = 47.14 minutes