The concentration of Iron in the galvanic (voltaic) cell Fe(s) + Mn²⁺(aq) ⟶ Fe²⁺(aq) + Mn(s) is 0.02297 M.
<h3>What is the Nernst Equation?</h3>
The Nernst equation enables us to identify the cell potential(voltage) in presence of non-standard conditions in a galvanic cell. It can be expressed by using the formula:
![\mathbf{E_{cell} = E_o - \dfrac{0.059}{n} \times log \dfrac{[Fe^+]}{[Mn^{2+}]}}](https://tex.z-dn.net/?f=%5Cmathbf%7BE_%7Bcell%7D%20%3D%20E_o%20-%20%5Cdfrac%7B0.059%7D%7Bn%7D%20%5Ctimes%20log%20%5Cdfrac%7B%5BFe%5E%2B%5D%7D%7B%5BMn%5E%7B2%2B%7D%5D%7D%7D)
where;
- n = Number of electrons = 2
= Initial voltage = 0.77 V
= Cell voltage = 0.78 V![\mathbf{[Mn^{2+}]}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5BMn%5E%7B2%2B%7D%5D%7D)
= Manganese concentration = 0.050 M
Replacing the values into the above equation, we have:
![\mathbf{0.78 = 0.77 - \dfrac{0.059}{2} \times log \dfrac{[Fe^{2+}]}{[0.050]}}](https://tex.z-dn.net/?f=%5Cmathbf%7B0.78%20%3D%200.77%20-%20%5Cdfrac%7B0.059%7D%7B2%7D%20%5Ctimes%20log%20%5Cdfrac%7B%5BFe%5E%7B2%2B%7D%5D%7D%7B%5B0.050%5D%7D%7D)
![\mathbf{0.78 -0.77= -0.0296\times log \dfrac{[Fe^{2+}]}{[0.050]}}](https://tex.z-dn.net/?f=%5Cmathbf%7B0.78%20-0.77%3D%20-0.0296%5Ctimes%20log%20%5Cdfrac%7B%5BFe%5E%7B2%2B%7D%5D%7D%7B%5B0.050%5D%7D%7D)
![\mathbf{log^{-1} (-0.3378) = \dfrac{[Fe^{2+}]}{[0.050]}}](https://tex.z-dn.net/?f=%5Cmathbf%7Blog%5E%7B-1%7D%20%28-0.3378%29%20%3D%20%5Cdfrac%7B%5BFe%5E%7B2%2B%7D%5D%7D%7B%5B0.050%5D%7D%7D)
Learn more about using the Nernst equation here:
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Prolog languages are logics that are used when creating programs that require artificial intelligence.
The prolog rule to define the predicate grandfather(x, y) is grandfather(X,Y) :- mother(M,Y), father(X,M); father(F,Y), father(X,F)
<h3>How to determine the prolog rule</h3>
From the question, we have the following definitions:
- mother(m, y): m is the mother of y
- father(f, x): f is the father of x
For x to be the grandfather of y, then either of the following definitions must be true
- m is the mother of y, and x is the father of m
- f is the father of y, and x is the father of f
Using the above highlights, the prolog rule would be
grandfather(X,Y) :-
mother(M,Y), father(X,M);
father(F,Y), father(X,F)
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C. A diverse way in which scientists study the natural world
Distribution centers enable retailers to carry less merchandise in individual stores.
<h3>What are distribution centers?</h3>
Distribution centers in business also known as warehouses are centers where goods for sale are kept in large quantities for onward distribution to retailers.
Distribution centers are very important to both the producer as well as the retailer.
Distribution centers ensure that the retailers are able to get the goods they sell at a discount price. It also ensures that the retailers do not have seek out the producers in their various factories for them to purchase the goods they need.
Thus, distribution centers enable retailers to carry less merchandise in individual stores.
For the producers, distribution centers serve as an outlet for the producers to get their good into the hands of retailers in large quantities. It also solves the problem of logistics for the producers.
In conclusion, distribution centers serve as temporary stores for goods.
Learn more about distribution centers at: brainly.com/question/23941356
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