[jjkwest1]

A typical bathtub can hold 97 gallons of water. Calculate the mass of natural gas that would need to be burned to heat the water for a tub of this size from 61 degrees fahrenheit to 101 degrees farenheit. assume that the natural gas is pure methane (CH4) and that the products of combustion are carbon dioxide and water (liquid).

part 2 : What volume of natural gas does this correspond to at 31 degree celsius and 1.6 atm?


I have no clue how to start this problem. When i first saw this question i was thinking that i could start this out with PV=nRT and solve for the number of moles and convert that to grams of methane however there was no pressure given. I'm really confused, can someone help me out with this thanks. Also for part 2 once you find the grams of methane then do you use the ideal gas law? thanks

[Yggdrasil]

Step 1:  Calculate the amount of heat required to warm the water from 61^oF to 101^oF.
Step 2:  Calculate the enthalpy of combustion of methane.

[jjkwest1]

i found the entahlpy for the combustion of methane to be -890.5 kj...however i dont know how you find the heat to raise the temp of the water. Also, how would you find the mass of methane from that info?

[sjb]

Step 0.5 define your gallon

Step 1:  Calculate the amount of heat required to warm the water from 61^oF to 101^oF.
Step 2:  Calculate the enthalpy of combustion of methane.

i found the entahlpy for the combustion of methane to be -890.5 kj.. Also, how would you find the mass of methane from that info?

-890.5 kJ for what quantity of methane, 1 molecule? 1 tonne?

however i dont know how you find the heat to raise the temp of the water.

E = m c  :delta: T (or equivalent, see http://www.google.com/cse?q=calorimetry&cx=partner-pub-4958982952381359%3Ashegok3d6wg for similar examples)

[jjkwest1]

E = m c  :delta: T (or equivalent, see http://www.google.com/cse?q=calorimetry&cx=partner-pub-4958982952381359%3Ashegok3d6wg for similar examples)
[/quote]

would m be the mass of methane?

[Borek]

You are heating methane, or water?

Check you notes or textbook on what m c ΔT is. Or google for a heat balance, tons of decent pages explaining the idea.

[jjkwest1]

Alright, so i think i know how to do this. Can anyone check to see if i did it right?

97 gallons to milliliters= 367183.8 ml   
367183.8 ml*1g/ml= 367183.8 g of water

i got the change in temperature from fahrenheit to celsius to be 22.22 degree celsius

the specific heat of water = .00418 kJ/ degree celsius *g

next i use the equation Q=mC(delta T)

i get=  (367183.8g)(.00418kJ/ degree celsius *g)(22.22 degree celsius) =  34103.88447 kJ


next i find the entalpy for the combustion of methane:

CH4 + 2O2   --->  CO2 + 2H2O

Delta H= 2(-286)+(-393.5)-(-75)
          = -890.5kJ/mole of CH4

then to find grams i do    34103.88447 kJ * (1 mole CH4/890.5 kJ) = 38.297 moles CH4

38.297 moles CH4 * (16.042 g CH4/ 1 mole CH4) = 614.4 g CH4

Also for the last part when they ask for the volume of the natural gas when it correspomds to 31 degree celsius and 1.6 atm, do i use PV=nRT for that since i know the pressure, temp and the number od moles? Thanks

[Borek]

I have not checked numbers, but approach seems correct. Yes, pV=nRT for a final touch.