Q: Which equation correctly represents the general mass balance for a system with accumulation?

$\text{IN} - \text{UIT} = \text{ACCUMULATIE}$

Q: A bathtub is being filled with water from a shower at a rate of $10 \ \text{kg/min}$, while water drains out at $8 \ \text{kg/min}$. What happens to the water level in the tub?

The water level rises because $\text{IN} > \text{UIT}$

Q: Given three input streams to a tank: $\dot{m}_1 = 196.7 \ \text{kg/hr}$, $\dot{m}_2 = 243.9 \ \text{kg/hr}$, and $\dot{m}_3 = 119.3 \ \text{kg/hr}$, what is the total output stream $\dot{m}_4$ if the process is stationary?

$\dot{m}_4 = 196.7 + 243.9 + 119.3 = 560.0 \ \text{kg/hr}$

Q: A solution contains $1 \ \text{wt}\%$ NaOH in water. You want to prepare $8 \ \text{wt}\%$ NaOH solution by mixing with pure water. If you choose the final stream to be $100 \ \text{kg/s}$, what is the correct mass balance equation for NaOH?

$X_{\text{NaOH},1} M_1 + X_{\text{NaOH},2} M_2 = X_{\text{NaOH},3} M_3$

Q: In a process, the input stream contains $10 \ \text{L/s}$ of $1 \ \text{M}$ ammonia solution. You want to dilute it to $0.6 \ \text{M}$ by adding water. What is the total final volumetric flow rate?

$\frac{10}{0.6} = 16.67 \ \text{L/s}$

Q: A process has three output streams with the following mass fractions of component A: $0.35$, $0.67$, and $0.1$. If the total output mass flow is $4.82 \ \text{kg/s}$, what is the mass flow of component A in the output?

$0.35 \times 4.82 + 0.67 \times 4.82 + 0.1 \times 4.82 = 5.82 \ \text{kg/s}$ (but this sum is not possible, as fractions must sum to 1)

Q: A distillation column splits air (79 mol% N$_2$, 21 mol% O$_2$) into two streams. The bottom stream contains 80 kmol/hr N$_2$ and is 95% of the total N$_2$ input. What is the total N$_2$ input?

$\frac{80}{0.95} = 84.21 \ \text{kmol/hr}$

Q: If a process stream contains $100 \ \text{kg/h}$ with $20 \ \text{wt}\%$ solute, how many kg of solute are present per hour?

$100 \times 0.20 = 20 \ \text{kg/h}$

Question 1

Which equation correctly represents the general mass balance for a system with accumulation?

Accepted Answer

$	ext{IN} - 	ext{UIT} = 	ext{ACCUMULATIE}$

Question 2

In a stationary (steady-state) process, what is the value of accumulation?

Accepted Answer

$	ext{ACCUMULATIE} = 0$

Question 3

A bathtub is being filled with water from a shower at a rate of $10 \ 	ext{kg/min}$, while water drains out at $8 \ 	ext{kg/min}$. What happens to the water level in the tub?

Accepted Answer

The water level rises because $	ext{IN} > 	ext{UIT}$

Question 4

Which of the following is a correct statement about mass and energy in a process?

Accepted Answer

Mass and energy cannot be created or destroyed; they are conserved.

Question 5

Given three input streams to a tank: $\dot{m}_1 = 196.7 \ 	ext{kg/hr}$, $\dot{m}_2 = 243.9 \ 	ext{kg/hr}$, and $\dot{m}_3 = 119.3 \ 	ext{kg/hr}$, what is the total output stream $\dot{m}_4$ if the process is stationary?

Accepted Answer

$\dot{m}_4 = 196.7 + 243.9 + 119.3 = 560.0 \ 	ext{kg/hr}$

Question 6

A solution contains $1 \ 	ext{wt}\%$ NaOH in water. You want to prepare $8 \ 	ext{wt}\%$ NaOH solution by mixing with pure water. If you choose the final stream to be $100 \ 	ext{kg/s}$, what is the correct mass balance equation for NaOH?

Accepted Answer

$X_{	ext{NaOH},1} M_1 + X_{	ext{NaOH},2} M_2 = X_{	ext{NaOH},3} M_3$

Question 7

In a process, the input stream contains $10 \ 	ext{L/s}$ of $1 \ 	ext{M}$ ammonia solution. You want to dilute it to $0.6 \ 	ext{M}$ by adding water. What is the total final volumetric flow rate?

Accepted Answer

$\frac{10}{0.6} = 16.67 \ 	ext{L/s}$

Question 8

Which method is commonly used to solve mass balance problems with two unknowns?

Accepted Answer

Substitution or elimination method

Question 9

A process has three output streams with the following mass fractions of component A: $0.35$, $0.67$, and $0.1$. If the total output mass flow is $4.82 \ 	ext{kg/s}$, what is the mass flow of component A in the output?

Accepted Answer

$0.35 	imes 4.82 + 0.67 	imes 4.82 + 0.1 	imes 4.82 = 5.82 \ 	ext{kg/s}$ (but this sum is not possible, as fractions must sum to 1)

Question 10

When converting a volumetric flow rate of a gas to a molar flow rate, which equation should be used?

Accepted Answer

$n = \frac{PV}{RT}$

Question 11

A distillation column splits air (79 mol% N$_2$, 21 mol% O$_2$) into two streams. The bottom stream contains 80 kmol/hr N$_2$ and is 95% of the total N$_2$ input. What is the total N$_2$ input?

Accepted Answer

$\frac{80}{0.95} = 84.21 \ 	ext{kmol/hr}$

Question 12

In a multi-component system, what is the sum of all mass fractions in a single stream?

Accepted Answer

$\sum_{i} x_i = 1$

Question 13

If a process stream contains $100 \ 	ext{kg/h}$ with $20 \ 	ext{wt}\%$ solute, how many kg of solute are present per hour?

Accepted Answer

$100 	imes 0.20 = 20 \ 	ext{kg/h}$

Question 14

Which of the following is NOT a step in the SPA (Systematic Problem Approach) for solving mass balance problems?

Accepted Answer

Guessing unknown values without equations

Question 15

A process has two input streams: Stream 1 is $8 \ 	ext{kg/s}$ of pure water, Stream 2 is $2 \ 	ext{kg/s}$ of pure sugar. What is the mass fraction of sugar in the combined output stream?

Accepted Answer

$\frac{2}{8+2} = 0.2$

Question 16

In a process with three output streams, the total output must equal the total input if the process is:

Accepted Answer

Stationary (steady-state)

Question 17

Which of the following best describes a component balance in a multi-component system?

Accepted Answer

The amount of each component in equals the amount out, assuming no accumulation.

Question 18

A gas stream of water vapor at $0.2 \ 	ext{bar}$ and $60^\circ 	ext{C}$ has a volumetric flow rate of $50 \ 	ext{m}^3$/h. What is the molar flow rate of water vapor? (Use $R = 0.08314 \ 	ext{bar} \cdot 	ext{L} / 	ext{mol} \cdot 	ext{K}$, $T = 333 \ 	ext{K}$)

Accepted Answer

$n = \frac{0.2 	imes 50000}{0.08314 	imes 333} = 36.2 \ 	ext{mol/h}$

Mass Balances in Chemical Processes: Principles and Applications

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