Question

A chemist fills a reaction vessel with 9.20 atm nitrogen monoxide (NO) gas, 9.15 atm chlorine (CI) gas, and 7.70 atm nitrosyl chloride (NOCI) gas at a temperature of 25.0°C. Under these conditions, calculate the reaction free energy AG for the following chemical reaction: 2NO(g) +CI (8) - 2NOCI (8) Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule

Answer 1

The reactions free energy
`\Delta G = -49.36 kJ`

Step-by-step explanation:

From the question we are told that

The pressure of (NO) is
`P_(NO) = 9.20 \ atm`

The pressure of (Cl) gas is
`P_(Cl) = 9.15 \ atm`

The pressure of nitrosly chloride (NOCl) is
`P_((NOCl)) = 7.70 \ atm`

The reaction is

`2NO_((g)) + Cl_2 (g)` ⇆
`2 NOCl_((g))`

From the reaction we can mathematically evaluate the
`\Delta G^o` (Standard state free energy ) as

`\Delta G^o = 2 \Delta G^o _(NOCl) - \Delta G^o _(Cl_2) - 2 \Delta G^o _(NO)`

The Standard state free energy for NO is constant with a value

`\Delta G^o _(NO) = 86.55 kJ/mol`

The Standard state free energy for
`Cl_2` is constant with a value

`\Delta G^o _(Cl_2) = 0kJ/mol`

The Standard state free energy for
`NOCl` is constant with a value

`\Delta G^o _(NOCl) =66.1kJ/mol`

Now substituting this into the equation

`\Delta G^o = 2 * 66.1 - 0 - 2 * 87.6`

`= -43 kJ/mol`

The pressure constant is evaluated as

`Q = (Pressure \ of \ product )/( Pressure \ of \ reactant )`

Substituting values

`Q = ((7.7)^2 )/((9.2)^2 (9.15) ) = (59.29)/(774.456)`

`= 0.0765`

The free energy for this reaction is evaluated as

`\Delta G = \Delta G^o + RT ln Q`

Where R is gas constant with a value of
`R = 8.314 J / K \cdot mol`

T is temperature in K with a given value of
`T = 25+273 = 298 K`

Substituting value

`\Delta G = -43 *10^(3) + 8.314 *298 * ln [0.0765]`

`= -43-6.36`

`\Delta G = -49.36 kJ`