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Chapter 8: Q 13-29MP (page 466)

Question: If 10kgof rock salt is placed in water, it dissolves at a rate proportional to the amount of salt still undissolved. If 2kgdissolve during the first 10minutes, how long will it be until only 2kgremain undissolved?

Short Answer

Expert verified

The time when only 2kg of rock salt remain undisclosed is 72.12 min. i.e. 62 min more

Step by step solution

01

Given Information

The amount of rock salt is 10kg and the amount of salt dissolved in 10 min is 2kg.

02

Integration formula

The integral of dx/x is given by In x + c.

03

Amount of Undisclosed Salt

The amount of undisclosed salt is (s0 -s) where the initial amount is s0.

Since, the rate of dissolving the salt is proportional to the amount of salt still undisclosed.

Integrate above equation.

Substitute 0 for t and 0 for s in Equation (1).

s0 = A

Substitute 10 for t and 2 for s in Equation (2).

Substitute for k and 2 for s in Equation (2).

The time when only 2kg of rock salt remain undisclosed is 72.12 min. i.e. 62 min more

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