Question

Assume that you can heat water with perfect insulation (all the heat from combustion of ethanol is transferred to water). What is the volume of ethanol required to heat 200 mL of water by 10 °C? The density of ethanol is 0.78 g/mL, the specific heat capacity of water is 4.184 J∙g−1∙°C−1and the heat of combustion of ethanol is -1368 kJ/mol. Show your work.

Answer 1

Answer:

volumme =0.36 ml

Explanation:

total heat required can be obtained by using following formula

$q= mC \Delta T$.......(1)

where,

m - mass of water,

C - specific heat capacity of water and = 4.184 j g^{-1} °C

$\Delta T$ - total change in temperature.  = 10°C

The density of water is 1 g/cc. hence, 200 mL of water is equal to 200 g

putting all value in the above equation (1)

q = 200*4.184* 10 ° = 8368 J.

Therefore total number of moles of ethanol required to supply 8368 J of heat is

$\frac {8368}{1368000} = 0.006117 moles.$

The molar mass of ethanol is 46 g/mol.

The mass of ethanol required is 46* 0.006117 = 0.28138 g

The density of ethanol is 0.78 g/ml.

The volume of ethanol required is

$\frac {0.28138}{0.78} = 0.36 ml$