0.5 mol of salt (NaCl) is dissolved in 4.5 mol of water. What is the increase in entropy
To find the increase in entropy, we need to understand the concept of entropy and how to calculate it.
Entropy (S) is a measure of the randomness or disorder of a system. In this case, we are interested in the change in entropy (∆S) when salt is dissolved in water.
The increase in entropy can be calculated using the equation:
∆S = S_f - S_i
Where ∆S is the change in entropy, S_f is the final entropy, and S_i is the initial entropy.
To calculate the final and initial entropy, we need to consider the entropy of the salt and water before and after mixing.
The entropy change when salt dissolves in water can be positive, negative, or zero, depending on the specific conditions. In general, the dissolution of a solid into a liquid usually leads to an increase in entropy.
To calculate the entropy change, we can use the formula:
∆S_solution = ∆S_salt + ∆S_water
The entropy change of the salt (∆S_salt) can be calculated using the equation:
∆S_salt = n*R*log(V_2/V_1)
Where n is the number of moles of the dissolved substance (salt), R is the ideal gas constant (8.314 J/(mol·K)), V_2 is the volume of the solution after dissolving the salt, and V_1 is the volume of the pure solvent (water) before adding the salt.
The entropy change of the water (∆S_water) can be calculated using the equation:
∆S_water = n*R*log(P_2/P_1)
Where n is the number of moles of the solvent (water), R is the ideal gas constant (8.314 J/(mol·K)), P_2 is the vapor pressure of the solution after dissolving the salt, and P_1 is the vapor pressure of the pure solvent (water) before adding the salt.
Given that 0.5 mol of salt is dissolved in 4.5 mol of water, we can substitute the values into the equations and calculate the entropy change. However, we need additional information such as the volumes and vapor pressures to obtain a numerical value for ∆S.