salt flux through the membrane of a reverse osmosis system Given salt mass transfer coefficient (K_s) = 1.3400 m/day; feed side salt concentration (C_1) = 23.0000 kg/m^3; permeate side salt concentration (C_2) = 0.8100 kg/m^3, determine the salt flux (F_s) in kg/m^2/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except F_s is given, so isolate F_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for F_s:

   $$F_{s} = K_s(C_1-C_2)$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 1.3400 m/day, feed side salt concentration (C_1) = 23.0000 kg/m^3, permeate side salt concentration (C_2) = 0.8100 kg/m^3.

4. Step 4 — Substitute the given values:

   $$F_{s} = K_s(C_1-C_2)$$

5. Step 5 — Evaluate:

   F_{s} = 29.7346\ \text{kg/m^2/day}

6. Step 6 — Check: returning F_s = 29.7346 kg/m^2/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 59.4692 — kept a factor of two that cancels in the correct rearrangement.
• 14.8673 — dropped that same factor in the other direction.
• 32.7081 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the membrane driven by concentration gradient Given feed side salt concentration (C_1) = 37.2000 kg/m^3; permeate side salt concentration (C_2) = 0.2700 kg/m^3; salt flux (F_s) = 79.1500 kg/m^2/day, determine the salt mass transfer coefficient (K_s) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except K_s is given, so isolate K_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for K_s:

   $$K_{s} = \dfrac{F_s}{C_1-C_2}$$

3. Step 3 — List the givens: feed side salt concentration (C_1) = 37.2000 kg/m^3, permeate side salt concentration (C_2) = 0.2700 kg/m^3, salt flux (F_s) = 79.1500 kg/m^2/day.

4. Step 4 — Substitute the given values:

   $$K_{s} = \dfrac{F_s}{C_1-C_2}$$

5. Step 5 — Evaluate:

   $$K_{s} = 2.1432\ \text{m/day}$$

6. Step 6 — Check: returning K_s = 2.1432 m/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4.2865 — kept a factor of two that cancels in the correct rearrangement.
• 1.0716 — dropped that same factor in the other direction.
• 2.3576 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the RO membrane used for permeate quality prediction Given salt mass transfer coefficient (K_s) = 1.4600 m/day; permeate side salt concentration (C_2) = 0.6300 kg/m^3; salt flux (F_s) = 2.3600 kg/m^2/day, determine the feed side salt concentration (C_1) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except C_1 is given, so isolate C_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for C_1:

   $$C_{1} = \dfrac{F_s}{K_s}+C_2$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 1.4600 m/day, permeate side salt concentration (C_2) = 0.6300 kg/m^3, salt flux (F_s) = 2.3600 kg/m^2/day.

4. Step 4 — Substitute the given values:

   $$C_{1} = \dfrac{F_s}{K_s}+C_2$$

5. Step 5 — Evaluate:

   C_{1} = 2.2464\ \text{kg/m^3}

6. Step 6 — Check: returning C_1 = 2.2464 kg/m^3 to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4.4929 — kept a factor of two that cancels in the correct rearrangement.
• 1.1232 — dropped that same factor in the other direction.
• 2.4711 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the membrane of a reverse osmosis system Given salt mass transfer coefficient (K_s) = 2.8600 m/day; feed side salt concentration (C_1) = 12.6000 kg/m^3; permeate side salt concentration (C_2) = 0.0500 kg/m^3, determine the salt flux (F_s) in kg/m^2/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except F_s is given, so isolate F_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for F_s:

   $$F_{s} = K_s(C_1-C_2)$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 2.8600 m/day, feed side salt concentration (C_1) = 12.6000 kg/m^3, permeate side salt concentration (C_2) = 0.0500 kg/m^3.

4. Step 4 — Substitute the given values:

   $$F_{s} = K_s(C_1-C_2)$$

5. Step 5 — Evaluate:

   F_{s} = 35.8930\ \text{kg/m^2/day}

6. Step 6 — Check: returning F_s = 35.8930 kg/m^2/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 71.7860 — kept a factor of two that cancels in the correct rearrangement.
• 17.9465 — dropped that same factor in the other direction.
• 39.4823 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the membrane driven by concentration gradient Given feed side salt concentration (C_1) = 9.4000 kg/m^3; permeate side salt concentration (C_2) = 0.3900 kg/m^3; salt flux (F_s) = 70.1900 kg/m^2/day, determine the salt mass transfer coefficient (K_s) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except K_s is given, so isolate K_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for K_s:

   $$K_{s} = \dfrac{F_s}{C_1-C_2}$$

3. Step 3 — List the givens: feed side salt concentration (C_1) = 9.4000 kg/m^3, permeate side salt concentration (C_2) = 0.3900 kg/m^3, salt flux (F_s) = 70.1900 kg/m^2/day.

4. Step 4 — Substitute the given values:

   $$K_{s} = \dfrac{F_s}{C_1-C_2}$$

5. Step 5 — Evaluate:

   $$K_{s} = 7.7902\ \text{m/day}$$

6. Step 6 — Check: returning K_s = 7.7902 m/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 15.5805 — kept a factor of two that cancels in the correct rearrangement.
• 3.8951 — dropped that same factor in the other direction.
• 8.5693 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the RO membrane used for permeate quality prediction Given salt mass transfer coefficient (K_s) = 1.9300 m/day; permeate side salt concentration (C_2) = 0.7700 kg/m^3; salt flux (F_s) = 81.9900 kg/m^2/day, determine the feed side salt concentration (C_1) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except C_1 is given, so isolate C_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for C_1:

   $$C_{1} = \dfrac{F_s}{K_s}+C_2$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 1.9300 m/day, permeate side salt concentration (C_2) = 0.7700 kg/m^3, salt flux (F_s) = 81.9900 kg/m^2/day.

4. Step 4 — Substitute the given values:

   $$C_{1} = \dfrac{F_s}{K_s}+C_2$$

5. Step 5 — Evaluate:

   C_{1} = 43.2519\ \text{kg/m^3}

6. Step 6 — Check: returning C_1 = 43.2519 kg/m^3 to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 86.5037 — kept a factor of two that cancels in the correct rearrangement.
• 21.6259 — dropped that same factor in the other direction.
• 47.5771 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the membrane of a reverse osmosis system Given salt mass transfer coefficient (K_s) = 1.7800 m/day; feed side salt concentration (C_1) = 30.0000 kg/m^3; permeate side salt concentration (C_2) = 0.1100 kg/m^3, determine the salt flux (F_s) in kg/m^2/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except F_s is given, so isolate F_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for F_s:

   $$F_{s} = K_s(C_1-C_2)$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 1.7800 m/day, feed side salt concentration (C_1) = 30.0000 kg/m^3, permeate side salt concentration (C_2) = 0.1100 kg/m^3.

4. Step 4 — Substitute the given values:

   $$F_{s} = K_s(C_1-C_2)$$

5. Step 5 — Evaluate:

   F_{s} = 53.2042\ \text{kg/m^2/day}

6. Step 6 — Check: returning F_s = 53.2042 kg/m^2/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 106.4 — kept a factor of two that cancels in the correct rearrangement.
• 26.6021 — dropped that same factor in the other direction.
• 58.5246 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the membrane driven by concentration gradient Given feed side salt concentration (C_1) = 35.6000 kg/m^3; permeate side salt concentration (C_2) = 0.0400 kg/m^3; salt flux (F_s) = 39.1700 kg/m^2/day, determine the salt mass transfer coefficient (K_s) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except K_s is given, so isolate K_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for K_s:

   $$K_{s} = \dfrac{F_s}{C_1-C_2}$$

3. Step 3 — List the givens: feed side salt concentration (C_1) = 35.6000 kg/m^3, permeate side salt concentration (C_2) = 0.0400 kg/m^3, salt flux (F_s) = 39.1700 kg/m^2/day.

4. Step 4 — Substitute the given values:

   $$K_{s} = \dfrac{F_s}{C_1-C_2}$$

5. Step 5 — Evaluate:

   $$K_{s} = 1.1015\ \text{m/day}$$

6. Step 6 — Check: returning K_s = 1.1015 m/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2.2030 — kept a factor of two that cancels in the correct rearrangement.
• 0.5508 — dropped that same factor in the other direction.
• 1.2117 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the RO membrane used for permeate quality prediction Given salt mass transfer coefficient (K_s) = 4.6900 m/day; permeate side salt concentration (C_2) = 0.1300 kg/m^3; salt flux (F_s) = 33.8800 kg/m^2/day, determine the feed side salt concentration (C_1) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except C_1 is given, so isolate C_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for C_1:

   $$C_{1} = \dfrac{F_s}{K_s}+C_2$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 4.6900 m/day, permeate side salt concentration (C_2) = 0.1300 kg/m^3, salt flux (F_s) = 33.8800 kg/m^2/day.

4. Step 4 — Substitute the given values:

   $$C_{1} = \dfrac{F_s}{K_s}+C_2$$

5. Step 5 — Evaluate:

   C_{1} = 7.3539\ \text{kg/m^3}

6. Step 6 — Check: returning C_1 = 7.3539 kg/m^3 to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 14.7078 — kept a factor of two that cancels in the correct rearrangement.
• 3.6769 — dropped that same factor in the other direction.
• 8.0893 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane

salt flux through the membrane of a reverse osmosis system Given salt mass transfer coefficient (K_s) = 4.7200 m/day; feed side salt concentration (C_1) = 36.0000 kg/m^3; permeate side salt concentration (C_2) = 0.6900 kg/m^3, determine the salt flux (F_s) in kg/m^2/day.

Start with the thinking

• The governing relation printed in this handbook section is Salt Flux through the Membrane.
• Everything except F_s is given, so isolate F_s symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Salt flux through the membrane in reverse osmosis is proportional to the salt concentration difference across the membrane.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_s = K_s (C_1 - C_2)$$

2. Step 2 — Rearrange symbolically for F_s:

   $$F_{s} = K_s(C_1-C_2)$$

3. Step 3 — List the givens: salt mass transfer coefficient (K_s) = 4.7200 m/day, feed side salt concentration (C_1) = 36.0000 kg/m^3, permeate side salt concentration (C_2) = 0.6900 kg/m^3.

4. Step 4 — Substitute the given values:

   $$F_{s} = K_s(C_1-C_2)$$

5. Step 5 — Evaluate:

   F_{s} = 166.7\ \text{kg/m^2/day}

6. Step 6 — Check: returning F_s = 166.7 kg/m^2/day to

   $$F_s = K_s (C_1 - C_2)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 333.3 — kept a factor of two that cancels in the correct rearrangement.
• 83.3316 — dropped that same factor in the other direction.
• 183.3 — rounded an intermediate value before the final step.

Reference: FE Handbook — Salt Flux through the Membrane