Question

In which of the following systems is(are) work done by the surroundings on the system? Assume pressure and temperature are constant.

$$\begin{gathered} \mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{2}{\mathbf{SO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{SO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{ }\mathbf{ }{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{4}{\mathbf{NH}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{7}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{4}{\mathbf{NO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ \mathbf{+}\mathbf{6}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ \mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathbf{ }\mathbf{ }{\mathbf{N}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{4}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{NO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ \mathbf{\left(}\mathbf{e}\mathbf{\right)}\mathbf{ }\mathbf{ }{\mathbf{CaCO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }\mathbf{Ca} \end{gathered}$$

Short answer

For system (a) and (c), work is done by the surroundings on the system. For the rest (b), (d), and (e) work is done by the system on the surroundings

Step-by-step solution

Introduction

Let the work done by the system be denoted by the symbol w. The pressure and volume are denoted by P and V respectively. The change in volume is ΔV and change in number of moles is Δn.

It has been assumed that the PV work can be done by gas only. Solids and liquids have been neglected.

If a balanced reaction contains a greater number of moles of product gases than that of moles of reactant gases which also means Δn positive or greater than zero, then there will be an expansion in volume due to the reaction. This indicates that work is done by the system surrounding it.

If a balanced reaction contains a greater number of moles of reactant gases than that of moles of product gases which also means Δn negative or less than zero, then there will be a contraction in volume due to the reaction. This indicates that work is done on the system by surrounding.

When there is no change in between the number of moles of reactant gases and the number of moles of product gases then, Δn=0. As a result, ΔV will be zero and as w=-P ΔV then, w will also be zero.

Determine the work done by the system or surrounding for part (a)

The number of moles of product gas = 2 and number of moles of reactant gas = 2+1=3

Therefore, Δn=2-3=-1<0. As Δn is negative, there will be contraction in volume due to this reaction. Therefore, the work will be done by the surrounding on the system.

Determine the work done by the system or surrounding for part (b)

the number of moles of product gas = 1 and number of moles of reactant gas = 0

Therefore, Δn=2-0=2>0. As Δn is positive, there will be expansion in volume due to this reaction. Therefore, work will be done by the system on the surrounding.

Determine the work done by the system or surrounding for part (c)

The number of moles of product gas =6+4=10 and number of moles of reactant gas = 7+4=11

Therefore, Δn=10-11=-1<0. As Δn is negative, there will be contraction in volume due to this reaction. Therefore, work will be done by the surrounding on the system.

Determine the work done by the system or surrounding for part (d) 

The number of moles of product gas = 2 and number of moles of reactant gas = 1

Therefore, Δn=2-1=1>0. As Δn is positive, there will be an expansion in volume due to this reaction. Therefore, work will be done by the system on the surrounding.

Determine the work done by system or surrounding for part (e)

The number of moles of product gas = 1 and number of moles of reactant gas = 0

Therefore, Δn=1-0=1>0. As Δn is positive, there will be an expansion in volume due to this reaction. Therefore, the work will be done by the system on the surrounding.