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

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

Answer 2

This question involves the concepts of the law of conservation of energy, specific heat capacity, and heat of combustion.

The volume of ethanol required to heat 200 mL of water by 10°C is "0.362 mL".

Applying the law of conservation of energy to this situation, we get:

$Heat\ of\ Combustion = Heat\ Absorbed\ by\ Water\\nH_c=mC\Delta T\\nH_c=\rho VC\Delta T$

where,

n = no. of moles of ethanol required = ?

$H_c$ = Heat of Combustion of Ethanol = -1368 KJ/mol (negative sign for release of heat)

$\rho$ = density of water = 1000 kg/m³

V = Volume of water = 200 mL = 2 x 10⁻⁴ m³

C = specific heat capacity of water = 4.200 KJ/kg.°C

ΔT = change in temperature = 10°C

Therefore,

$n = \frac{(1000\ kg/m^3)(2\ x\ 10^{-4}\ m^3)(4.2\ KJ/kg.^oC)(10^oC)}{1368\ KJ/mol}$

n = 0.0061 mole

For the mass of ethanol required:

m = (n)(molar mass of ethanol)

m = (0.0061 mole)(46 g/mol)

m = 0.282 g

Now, we will calculate the volume of ethanol required:

$Volume = \frac{m}{Denisty}\\\\Volume = \frac{0.282\ g}{0.78\ g/mL}$

Volume = 0.362 mL

Learn more about the law of conservation of energy here:

brainly.com/question/20971995?referrer=searchResults

The attached picture explains the law of conservation of energy.