Question

How much heat is required to convert 2.73 g g of water at 32.0 ∘ C ∘C to steam at 100.0 ∘ C ∘C ? (Δ H vap ( H 2 O)=40.7kJ/mol,Heatcapacity( H 2 O)=4.184J/g ∘ C) (ΔHvap(H2O)=40.7kJ/mol,Heatcapacity(H2O)=4.184J/g∘C) Express your answer with the appropriate units.

Answer 1

Q = 7898.38 J = 7.898 KJ

Step-by-step explanation:

• Q = mCΔT + ΔHv

∴ ΔHv H2O = 47 KJ/mol = 47000 J/mol

∴ molar mass H2O = 18.015 g/mol

⇒ ΔHv H2O = (47000 J/mol)*(mol/18.015 g) = 2608.94 J/g

∴ m H2O = 2.73 g

⇒ ΔHv H2O = (2.73 g)(2608.94 J/g) = 7122.406 J

∴ C H2O = 4.18 J/g°C

∴ ΔT = 100 - 32 = 68°C

⇒ Q = (2.73 g)(4.18 J/g°C)(68°C) + 7122.406 J

⇒ Q = 775.975 J + 7122.406 J

⇒ Q = 7898.38 J

Answer 2

We need 6942.7 J of heat

Step-by-step explanation:

Step 1: Data given

Mass of water = 2.73 grams

Initial temperature of water = 32.0 °C

Final temperature of water = 100 °C

Heat capacity of water = 4.184 J/g°C

ΔHvap(H2O) = 40.7kJ/mol

Step 2 : Calculate heat required to heat water from 32.0 °C to 100 °C

Q = m*c*ΔT

⇒with Q = the heat required = TO BE DETERMINED

⇒with m= the mass of water = 2.73 grams

⇒with c = the specific heat of water = 4.184 J/g°C

⇒with ΔT = The change of temperature = T2 - T1 = 100 °C - 32. 0°C = 68.0 °C

Q = 2.73 * 4.184 * 68.0 °C

Q = 776.7 J

Step 3: Calculate moles H2O

Moles H2O = mass H2O / molar mass H2O

Moles H2O = 2.73 grams / 18.02 g/mol

Moles H2O = 0.1515 moles

Step 4: Calculate heat required to change water from liquid to gas phase

Q = moles H2O*ΔHvap(H2O)

Q = 0.1515 moles * 40700J/mol

Q = 6166 J

Step 5 : Calculate the total heat required

Q = 776.7 J + 6166 J

Q = 6942.7 J

We need 6942.7 J of heat