Answer:
137639.472 J
Explanation:
Given, Mass of water = 1 kg = 1000 g
Molar mass of water = 18.0153 g/mol
The formula for the calculation of moles is shown below:
[tex]moles = \frac{Mass\ taken}{Molar\ mass}[/tex]
Thus,
[tex]Moles= \frac{1000\ g}{18.0153\ g/mol}[/tex]
[tex]Moles\ of\ water= 55.508\ mol[/tex]
Pressure = 1.0 atm
Temperature = 25 °C
The conversion of T( °C) to T(K) is shown below:
T(K) = T( °C) + 273.15
So,
T₁ = (25 + 273.15) K = 298.15 K
Using ideal gas equation as:
[tex]PV=nRT[/tex]
where,
P is the pressure
V is the volume
n is the number of moles
T is the temperature
R is Gas constant having value = 0.0821 L.atm/K.mol
Applying the equation as:
1.0 atm × V = 55.508 mol × 0.0821 L.atm/K.mol × 298.15 K
⇒V = 1358.7312 L
The expression for the calculation of work done by the surroundings is shown below as:
[tex]w=P\times \Delta V[/tex]
Where, P is the pressure
[tex]\Delta V[/tex] is the change in volume
From the question,
[tex]\Delta V[/tex] = 1358.7312 - 0 L = 1358.7312 L
P = 1.0 atm
[tex]w=1.0\times1358.7312\ atmL[/tex]
Also, 1 atmL = 101.3 J
So,
[tex]w=1.0\times1358.7312\times 101.3\ J=137639.472\ J[/tex]
