How to Solve a Material Balance Problem for Two Liquids A and B?

In summary: Thank you for your help. Ohk, thank you :) i will check it again and contact you if i need help. Thank you for your help.
  • #1
nahian taskin
14
0
Two liquids, A and B, are mixed together. A is 5.00% solids, the rest water. B is 11.0% solids, the rest water. To the mixture is added 18.5 kg of bone-dry solids resulting in a mixture of 2 150 kg containing 8.25% solids. What were the original amounts of the liquids A and B?
 
Physics news on Phys.org
  • #2
How many equations in how many unknowns?
 
  • #3
2 unknown. A and B.
 
  • #4
one example related to
Q.Anna's Purification Co. produces drinking water from saltwater by partially freezing the saltwater to create salt-free ice and a brine solution. Tf saltwater is 3.50% salt by mass and the brine solution is fow1d to be an 8.00% concentrate by mass, determine how many kilograms of saltwater must be processed to form 2.00 kg of ice.
Ans: Eqauation: input= output
Overall balance : S = B + 2.00
salt balance : 0.035S = 0.08B
water balance : 0.965S = 0.920B + 2.00
then solve for S and B.
 
  • #5
Bystander said:
How many equations in how many unknowns?
one example related to
Q.Anna's Purification Co. produces drinking water from saltwater by partially freezing the saltwater to create salt-free ice and a brine solution. Tf saltwater is 3.50% salt by mass and the brine solution is fow1d to be an 8.00% concentrate by mass, determine how many kilograms of saltwater must be processed to form 2.00 kg of ice.
Ans: Eqauation: input= output
Overall balance : S = B + 2.00
salt balance : 0.035S = 0.08B
water balance : 0.965S = 0.920B + 2.00
then solve for S and B.
 
  • #6
In terms of A and B, what is the total mass of the final mixture?

In terms of A and B, what is the mass of solids in the final mixture?

Chet
 
  • #7
Chestermiller said:
In terms of A and B, what is the total mass of the final mixture?

In terms of A and B, what is the mass of solids in the final mixture?

Chet
initial amount of A n B in the total mixture. How much kg of A and B was added in the mixture
 
  • #8
Chestermiller said:
In terms of A and B, what is the total mass of the final mixture?

In terms of A and B, what is the mass of solids in the final mixture?

Chet
Answers for this question is, A = 1260 kg, B = 872 kg
 
  • #9
nahian taskin said:
initial amount of A n B in the total mixture. How much kg of A and B was added in the mixture
I have no idea what you are saying here. Can you please answer the questions I asked (in the form of equations).

Chet
 
  • #10
Chestermiller said:
I have no idea what you are saying here. Can you please answer the questions I asked (in the form of equations).

Chet
No equations are given. From this, We have to make our own equation to get the solution.
I have tried with this equation:
For solid : 0.05A+ 0.11B = 18.5+ 2150(0.08125)
For Water: 0.95A+ 0.89B = 2150(0.9175)
solve the equations.
but i wrong answer,which means something is wrong in my equation
 
  • #11
nahian taskin said:
No equations are given. From this, We have to make our own equation to get the solution.
I have tried with this equation:
For solid : 0.05A+ 0.11B = 18.5+ 2150(0.08125)
For Water: 0.95A+ 0.89B = 2150(0.9175)
solve the equations.
but i wrong answer,which means something is wrong in my equation
how many equations it can be here, that's the confusion because i don't know wether its a batch process or rate process.
 
  • #12
nahian taskin said:
how many equations it can be here, that's the confusion because i don't know wether its a batch process or rate process.
Batch process : total input = total output.
Rate process: rate of input- rate of output= rate of accumulation.
if the rate process is uniform then ,
rate of input= rate of output.
 
  • #13
nahian taskin said:
No equations are given. From this, We have to make our own equation to get the solution.
I have tried with this equation:
For solid : 0.05A+ 0.11B = 18.5+ 2150(0.08125)
For Water: 0.95A+ 0.89B = 2150(0.9175)
solve the equations.
but i wrong answer,which means something is wrong in my equation
This is what I was looking for. Your formulation is very close to being correct. There are just a couple of minor errors.

1. In the solid equation, are you sure that 18.5 belongs on the right hand side of the equation?
2. In the water equation, recheck that 0.9175. There's an arithmetic error.

Chet
 
  • #14
Chestermiller said:
This is what I was looking for. Your formulation is very close to being correct. There are just a couple of minor errors.

1. In the solid equation, are you sure that 18.5 belongs on the right hand side of the equation?
2. In the water equation, recheck that 0.9175. There's an arithmetic error.

Chet
if 8.25% is solid then (100-8.25)% is water which is 91.75%
and i tried by giving 18.5 on the left hand side, but answer didnt came. It was more far than the actual answer.
 
  • #15
nahian taskin said:
if 8.25% is solid then (100-8.25)% is water which is 91.75%
and i tried by giving 18.5 on the left hand side, but answer didnt came. It was more far than the actual answer.
in the first equation i made a mistake it is 2150(0.0825) not 0.08125
 
  • #16
nahian taskin said:
in the first equation i made a mistake it is 2150(0.0825) not 0.08125

I know. I just noticed that. Do you get the right answer now with the 18.5 on the left?

Chet
 
  • #17
Chestermiller said:
I know. I just noticed that. Do you get the right answer now with the 18.5 on the left?

Chet
No, i didnt. I am now trying with by corrcting that value in the equation
 
  • #18
nahian taskin said:
No, i didnt. I am now trying with by corrcting that value in the equation
Didnt came again :( with this value .
somewhere is wrong, i don't know where!
 
  • #19
Here are the equations I solved, and I got the correct answer:

For solid : 0.05A+ 0.11B + 18.5 = 2150(0.0825)
For Water: 0.95A+ 0.89B = 2150(0.9175)

If you didn't get the correct answer using these equations, then you need to check your algebra.

Chet
 
  • #20
i was checking by putting the actual value in the equation then i get for the 1st equation , 18.5 would on left side .
and my second equation is wrong.
Chestermiller said:
Here are the equations I solved, and I got the correct answer:

For solid : 0.05A+ 0.11B + 18.5 = 2150(0.0825)
For Water: 0.95A+ 0.89B = 2150(0.9175)

If you didn't get the correct answer using these equations, then you need to check your algebra.

Chet
Ohk, thank you :)
 

Related to How to Solve a Material Balance Problem for Two Liquids A and B?

What is a material balance problem?

A material balance problem is a type of mathematical problem that is commonly encountered in various scientific fields, such as chemistry, physics, and engineering. It involves determining the amount of a substance or component in a system by considering the inputs, outputs, and accumulation of that substance within the system.

Why is material balance important?

Material balance is important because it allows scientists to understand and quantify the changes in a system over time. By using material balance equations, scientists can track the movement of substances within a system and make predictions about future behavior. This is crucial for many industrial processes, environmental studies, and other scientific investigations.

What are the key assumptions made in material balance calculations?

There are several key assumptions made in material balance calculations, including the assumption of a closed system (no inputs or outputs), the assumption of steady-state conditions (no changes in the system over time), and the assumption of conservation of mass (the total mass of the system remains constant).

How is material balance used in real-world applications?

Material balance is used in a wide range of real-world applications, including chemical process design, environmental pollution monitoring, and oil and gas production. It is also used in various research studies to understand the behavior of natural systems and to develop new technologies.

What are some common challenges in solving material balance problems?

Solving material balance problems can be challenging due to the complexity of the systems involved and the various assumptions that need to be made. The accuracy of the results also depends on the accuracy of the input data, which can be difficult to obtain in some cases. Additionally, material balance problems may involve multiple variables and equations, making them time-consuming to solve by hand.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Biology and Chemistry Homework Help
Replies
1
Views
2K
  • Mechanical Engineering
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
51K
Replies
11
Views
7K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Replies
3
Views
1K
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
893
  • Nuclear Engineering
Replies
3
Views
1K
Back
Top