Question

Calculate the Gibbs energy of mixing (in kJ) when 1.00 mol C6H14 (hexane) is mixed with 1.00 mol C7H16 (heptane) at 298 K; treat the solution as ideal.

Answer 1

The Gibbs energy of mixing when 1.00 mol C6H14 (hexane) is mixed with 1.00 mol C7H16 (heptane) at 298 K is -3.891 kJ/mol.

Step-by-step explanation:

The Gibbs energy of mixing can be calculated using the equation:

ΔG_mix = RT(xlnx + (1-x)ln(1-x))

Where:

• ΔG_mix is the Gibbs energy of mixing
• R is the ideal gas constant (8.314 J/(mol·K))
• T is the temperature in Kelvin
• x is the mole fraction of hexane

In this case, we have equal moles of hexane and heptane, so the mole fraction of hexane (x) is 0.5.

Plugging in the values, we get:

ΔG_mix = (8.314 J/(mol·K) * 298 K) * (0.5ln(0.5) + (1-0.5)ln(1-0.5))

ΔG_mix = -3.891 kJ/mol

Therefore, the Gibbs energy of mixing when 1.00 mol C6H14 (hexane) is mixed with 1.00 mol C7H16 (heptane) at 298 K is -3.891 kJ/mol.