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 $$\text{IN} \u003e \text{UIT}$$

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 $$	ext{IN} \u003e 	ext{UIT}$$

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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