Thermodynamics

NCERT Solution

Part 1

Question 1: A thermodynamic state function is a quantity

Used to determine heat changes
Whose value is independent of path
Used to determine pressure volume work
Whose value depends on temperature only

Answer: (b) Whose value is independent of path

Question 2: For the process to occur under adiabatic conditions, the correct condition is

ΔT = 0
Δp = 0
q = 0
w = 0

Answer: (c) q = 0

Question 3: The enthalpies of all elements in their standard states are

Unity
Zero
< zero
Different for each element

Answer: (b) zero

Question 4: ΔU^Θ of combustion of methane is – X kJ mol^-1. The value of ΔH^Θ is

= ΔU^Θ
> ΔU^Θ
< ΔU^Θ
= 0

Answer: Balanced chemical equation for combustion of methane is as follows:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)

In this reaction, there are 3 moles of gaseous reactants and 1 mole of gaseous products

So, Δn_g = 1 – 3 = - 2

We know, ΔH = ΔU + Δn_gRT

Substituting the values, we have:

ΔH = ΔU – 2RT

Or, ΔU = ΔH + 2RT

This equation means that ΔH < ΔU

So correct answer is option (c)

Question 5: The enthalpy of combustion of methane, graphite and dihydrogen at 298 K are, - 890.3 kJ mol^-1, - 393.5 kJ mol^-1 and – 285.8 kJ mol^-1. Enthalpy of formation of CH₄(g) will be

-74.8 kJ mol^-1
-52.27 kJ mol^-1
+74.8 kJ mol^-1
+52.26 kJ mol^-1

Answer: Balanced equation for combustion of methane, graphite and dihydrogen are given below in respective order

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)

C(g) + O₂(g) → CO₂(g)

H₂ + `1/2`O₂(g) → H₂O(l)

We can get the equation for formation of methane if add above equations as follows:

Equation (2) + 2 × equation (3) - equation (1)

Addition of LHS of equations:

C + O₂ + 2(H₂ + `1/2`O₂) – (CH₄ + 2O₂)

= C + O₂ + 2H₂ + O₂ - CH₄ - 2O₂

= C + 2H₂ - CH₄

Addition of RHS of equations:

CO₂ + 2H₂O – CO₂ - 2H₂ = 0

So, C + 2H₂ - CH₄ = 0

Or, C + 2H₂ = CH₄

Now, enthalpy of formation of methane can be calculated as follows:

Equation (2) + 2 × equation (3) - equation (1)

= -393.5 – 2 × 285.8 + 890.3 = -393.5 – 571.6 + 890.3 = -74.8 kJ mol^-1

So, correct answer is option (a)

Question 6: A reaction, A + B → C + D + q is found to have a positive entropy change. The reaction will be

Possible at high temperature
Possible only at low temperature
Not possible at any temperature
Possible at any temperature

Answer: (d) Possible at any temperature

Question 7: In a process, 701 J of heat is absorbed by a system and 394 J of work is done by the system. What is the change in internal energy for the process?

Answer: ΔU = q + w

= 701 – 394 (work is negative because it is done by the system)

= 307 J

Question 8: The reaction of cyanamide, NH₂CN (s), with dioxygen was carried out in a bomb calorimeter, and ΔU was found to be -742.7 kJ mol^-1 at 298 K. Calculate the enthalpy change for the reaction at 298 K.

NH₂CN(s) + `3/2`O₂(g) → CO₂(g) + H₂O(l)

Answer: Given, ΔU = -742.7 kJ mol^-1, T = 298 K.

R = 8.314 × 10^-3 J K^-1mol^-1

Δn_g = `2-3/2=1/2` mol

ΔH = ΔU + Δn_gRT

`= -742.7 + 1/2xx8.314xx10^(-3)xx298`

`=-742.70.004157xx298=-742.7+1.24=741.46` kJ

Question 9: Calculate the number of kJ of heat necessary to raise the temperature of 60.0 g of aluminium from 35°C to 55°C. Molar heat capacity of Al is 24 J mol^-1 K^-1.

Answer: Number of moles of Al (m) = `(60)/(27)=2.22` mol

Molar heat capacity (C) = 24 J mol^-1 K^-1

ΔT = 55 – 35 = 20°C = 20 K

Heat evolved q = C × m × T

= 24 × 2.22 × 20 = 1065.6 J = 1.067 kJ

Question 10: Calculate the enthalpy change on freezing of 1.0 mol of water at 10.0°C to ice at -10.0°C

Δ_fusH = 6.03 kJ mol^-1 at 0°C.

C_p[H₂O(l)] = 75.3 J mol^-1 K^-1

C_p[H₂O(s)] = 36.8 J mol^-1 K^-1

Answer: This change can be represented by following diagram:

According to Hess's Law:

ΔH = ΔH₁ + ΔH₂ + ΔH₃

Now, ΔH₁ = 75.3 J mol^-1 K^-1(10 K) = 753 J mol^-1

ΔH₂ = -6.03 kJ mol^-1 = -6030 J mol^-1

(sign changed to negative due to solidification)

ΔH₃ = 36.8 J mol^-1 K^-1 (-10 K) = - 368 J mol^-1

Now, ΔH = 753 – 6030 – 368 = -5645 J = - 5.654 kJ mol^-1

Question 11: Enthalpy of combustion of carbon to CO₂ is -393.5 kJ mol^-1. Calculate the heat released upon formation of 35.2 g of CO₂ from carbon and dioxygen gas.

Answer: Balanced equation for combustion of carbon is as follows:

C(s) + O₂ → CO₂(g)

Given: ΔH = - 393.5 kJ

Molar mass of carbon dioxide = 44 g

Since combustion of 44 g of CO₂ gives 393.5 kJ

Hence, combustion of 356.2 g of CO₂ will give

`(393.5)/(44)xx35.2=314.8` kJ