A tank originally contains 500 L of water with a salt concentration of 2 grams per liter.Water with a concentration of 1 gram/liter is then poured into the tank at a rate of3 L/min and the well stirred mixture is allowed to flow out of the tank at the same rate.a) Find a formula for Q(t), the quantity of salt in the tank after t minutes.b) Find the limiting quantity of salt in the tank as t → co

Answered: A tank originally contains 500 L of…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Question

A tank originally contains 500 L of water with a salt concentration of 2 grams per liter.
Water with a concentration of 1 gram/liter is then poured into the tank at a rate of
3 L/min and the well stirred mixture is allowed to flow out of the tank at the same rate.
a) Find a formula for Q(t), the quantity of salt in the tank after t minutes.
b) Find the limiting quantity of salt in the tank as t → co

Expert Solution

Step 1

the rate of change of a quantity over time. In this case, the quantity being described is the amount of salt in the tank, and the rate of change is described by the differential equation:

dQ/dt = 3 * (2 - 1) = 3

where dQ/dt represents the rate of change of the quantity of salt in the tank, 2 - 1 = 1 represents the difference in the concentration of salt between the water that is flowing out and the water that is being added, and 3 represents the rate at which the water is being added and flowing out. The solution to this differential equation,

Q(t) = Q(0) + 3t

This gives us the formula for the quantity of salt in the tank after t minutes.

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions