A saturated solution of Na2SO4, with excess of the solid, is present at equilibrium with its vapor in a closed vessel. (a) How many phases and components are present? (b) What is the number of degrees of freedom o the system? Identify the independent variables.
Suppose that the solution is not saturated. (c) How many phases and components are present? (d) What is the number of degrees of freedom of the system? Identify the independent variables.
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*So I think that F=C-P+2 and C=N-R, but I'm not sure.
I know Na2SO4 dissociates to 2 Na+ and SO4^2-, and I think that the difference between the questions is that the first is 3 phases and the second is 2 phases. Other than that, I'm confused on how this needs to be done, and why.
no. of componenents = 2 (Na2SO4 and water - as each phase can be described by these two components only)
no. of phases = 3 ( solid and liquid and vapor)
degrees of freedom = 2-3+2 = 1
Shut up
Answers to the questions
I'm confused how does Na2SO4 having 2 components?
It doesn’t have two components. H2O is the second component
To solve this problem, let's break it down step by step.
(a) In a saturated solution of Na2SO4 with excess solid, there are three phases present: solid Na2SO4, liquid Na2SO4 solution, and vapor (gas). As for the components, we need to consider the independent chemical species. The Na2SO4 can dissociate into two ions: Na+ and SO4^2-. Therefore, there are three components present: Na+, SO4^2-, and H2O (since the solution is aqueous).
(b) The number of degrees of freedom (F) of a system can be calculated using the formula F = C - P + 2, where C is the number of components and P is the number of phases. In this case, we have C = 3 (Na+, SO4^2-, and H2O) and P = 3 (solid, liquid, and vapor). Plugging these values into the formula, we get F = 3 - 3 + 2 = 2. This means that the system has two degrees of freedom. The independent variables can be any two variables, such as temperature and pressure, that can be changed without disturbing the phases and compositions.
Now let's consider the unsaturated solution:
(c) In an unsaturated solution of Na2SO4, there are only two phases present: the solid Na2SO4 and the liquid Na2SO4 solution. The vapor phase is not present since the solution is not saturated. The components remain the same: Na+, SO4^2-, and H2O.
(d) To calculate the degrees of freedom, we follow the same formula: F = C - P + 2. Now we have C = 3 (Na+, SO4^2-, and H2O) and P = 2 (solid and liquid). Plugging these values into the formula, we get F = 3 - 2 + 2 = 3. Therefore, the system has three degrees of freedom. The independent variables can be any three variables, such as temperature, pressure, and composition, that can be changed without altering the number of phases.
In summary:
(a) Saturated solution: 3 phases (solid, liquid, vapor), 3 components (Na+, SO4^2-, H2O), 2 degrees of freedom (independent variables may be temperature and pressure).
(b) Unsaturated solution: 2 phases (solid, liquid), 3 components (Na+, SO4^2-, H2O), 3 degrees of freedom (independent variables may be temperature, pressure, and composition).