/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 97 Calculate the ratio of \(\left[\... [FREE SOLUTION] | 91影视

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Chapter 17: Problem 97

Calculate the ratio of \(\left[\mathrm{Ca}^{2+}\right]\) to \(\left[\mathrm{Fe}^{2+}\right]\) in a lake in which the water is in equilibrium with deposits of both \(\mathrm{CaCO}_{3}\) and \(\mathrm{FeCO}_{3}\). Assume that the water is slightly basic and that the hydrolysis of the carbonate ion can therefore be ignored.

Short Answer

Expert verified
The ratio of [Ca虏鈦篯 to [Fe虏鈦篯 in the lake water in equilibrium with deposits of CaCO鈧� and FeCO鈧� is approximately 106.66. This was determined by using the solubility product expressions for both calcium carbonate and iron carbonate and dividing K鈧�(CaCO鈧�) by K鈧�(FeCO鈧�).

Step by step solution

01

Write the balanced dissolution equilibrium reactions for CaCO鈧� and FeCO鈧�

CaCO鈧�(s) 鈬� Ca虏鈦�(aq) + CO鈧兟测伝(aq) FeCO鈧�(s) 鈬� Fe虏鈦�(aq) + CO鈧兟测伝(aq)
02

Set up and apply the solubility product expressions

For both dissolution equilibria reactions, we know that the solubility product (K鈧�) is equal to the product of the concentrations of the ions in equilibrium with the solid compound. For calcium carbonate: K鈧�(CaCO鈧�) = [Ca虏鈦篯[CO鈧兟测伝] For iron carbonate: K鈧�(FeCO鈧�) = [Fe虏鈦篯[CO鈧兟测伝]
03

Solve for the ratio of the concentrations [Ca虏鈦篯 to [Fe虏鈦篯

We want to find the ratio of [Ca虏鈦篯 to [Fe虏鈦篯, which can be written as: 螕 = [Ca虏鈦篯 / [Fe虏鈦篯 In order to find this ratio, we can first divide the solubility product expression for CaCO鈧� by that for FeCO鈧�: K鈧�(CaCO鈧�) / K鈧�(FeCO鈧�) = ([Ca虏鈦篯[CO鈧兟测伝]) / ([Fe虏鈦篯[CO鈧兟测伝]) Notice that the [CO鈧兟测伝] terms cancel out from both numerator and denominator: K鈧�(CaCO鈧�) / K鈧�(FeCO鈧�) = [Ca虏鈦篯 / [Fe虏鈦篯 So, 螕 = K鈧�(CaCO鈧�) / K鈧�(FeCO鈧�)
04

Use the provided solubility product values to determine 螕

Values for the solubility products can be found in a reference table or textbooks: K鈧�(CaCO鈧�) = 3.36 脳 10鈦烩伖 K鈧�(FeCO鈧�) = 3.15 脳 10鈦宦孤� Now, we can plug in these values into our expression for 螕: 螕 = (3.36 脳 10鈦烩伖) / (3.15 脳 10鈦宦孤�) = 106.66 So, the ratio of [Ca虏鈦篯 to [Fe虏鈦篯 in the lake water in equilibrium with deposits of CaCO鈧� and FeCO鈧� is approximately 106.66.

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