osmotic pressure of solutions of electrolytes for a saline feedwater Given number of ions per molecule (Phi) = 3.0000; molar concentration (M) = 0.3800 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 281.0 K, determine the osmotic pressure (pi) in atm.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except pi is given, so isolate pi 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for pi:

   $$\pi = \Phi M R T$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 3.0000, molar concentration (M) = 0.3800 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 281.0 K.

4. Step 4 — Substitute the given values:

   $$\pi = 3.0000 0.3800 0.0821 281.0$$

5. Step 5 — Evaluate:

   $$\pi = 26.2999\ \text{atm}$$

6. Step 6 — Check: returning pi = 26.2999 atm to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 52.5998 — kept a factor of two that cancels in the correct rearrangement.
• 13.1500 — dropped that same factor in the other direction.
• 28.9299 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure calculation for an electrolyte solution in RO design Given number of ions per molecule (Phi) = 2.0000; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 300.0 K; osmotic pressure (pi) = 57.4800 atm, determine the molar concentration (M) in mol/L.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except M is given, so isolate M 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for M:

   $$M = \dfrac{\pi}{\Phi R T}$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 2.0000, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 300.0 K, osmotic pressure (pi) = 57.4800 atm.

4. Step 4 — Substitute the given values:

   $$M = \dfrac{57.4800}{2.0000 0.0821 300.0}$$

5. Step 5 — Evaluate:

   $$M = 1.1669\ \text{mol/L}$$

6. Step 6 — Check: returning M = 1.1669 mol/L to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 2.3337 — kept a factor of two that cancels in the correct rearrangement.
• 0.5834 — dropped that same factor in the other direction.
• 1.2836 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure of an electrolyte feed to a membrane system Given number of ions per molecule (Phi) = 3.0000; molar concentration (M) = 0.4310 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; osmotic pressure (pi) = 41.0200 atm, determine the absolute temperature (T) in K.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except T is given, so isolate T 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for T:

   $$T = \dfrac{\pi}{\Phi M R}$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 3.0000, molar concentration (M) = 0.4310 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, osmotic pressure (pi) = 41.0200 atm.

4. Step 4 — Substitute the given values:

   $$T = \dfrac{41.0200}{3.0000 0.4310 0.0821}$$

5. Step 5 — Evaluate:

   $$T = 386.4\ \text{K}$$

6. Step 6 — Check: returning T = 386.4 K to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

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

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure of solutions of electrolytes for a saline feedwater Given number of ions per molecule (Phi) = 4.0000; molar concentration (M) = 0.0950 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 286.0 K, determine the osmotic pressure (pi) in atm.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except pi is given, so isolate pi 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for pi:

   $$\pi = \Phi M R T$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 4.0000, molar concentration (M) = 0.0950 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 286.0 K.

4. Step 4 — Substitute the given values:

   $$\pi = 4.0000 0.0950 0.0821 286.0$$

5. Step 5 — Evaluate:

   $$\pi = 8.9226\ \text{atm}$$

6. Step 6 — Check: returning pi = 8.9226 atm to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 17.8453 — kept a factor of two that cancels in the correct rearrangement.
• 4.4613 — dropped that same factor in the other direction.
• 9.8149 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure calculation for an electrolyte solution in RO design Given number of ions per molecule (Phi) = 3.0000; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 278.0 K; osmotic pressure (pi) = 25.2200 atm, determine the molar concentration (M) in mol/L.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except M is given, so isolate M 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for M:

   $$M = \dfrac{\pi}{\Phi R T}$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 3.0000, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 278.0 K, osmotic pressure (pi) = 25.2200 atm.

4. Step 4 — Substitute the given values:

   $$M = \dfrac{25.2200}{3.0000 0.0821 278.0}$$

5. Step 5 — Evaluate:

   $$M = 0.3683\ \text{mol/L}$$

6. Step 6 — Check: returning M = 0.3683 mol/L to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 0.7367 — kept a factor of two that cancels in the correct rearrangement.
• 0.1842 — dropped that same factor in the other direction.
• 0.4052 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure of an electrolyte feed to a membrane system Given number of ions per molecule (Phi) = 1.0000; molar concentration (M) = 0.3890 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; osmotic pressure (pi) = 30.0300 atm, determine the absolute temperature (T) in K.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except T is given, so isolate T 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for T:

   $$T = \dfrac{\pi}{\Phi M R}$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 1.0000, molar concentration (M) = 0.3890 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, osmotic pressure (pi) = 30.0300 atm.

4. Step 4 — Substitute the given values:

   $$T = \dfrac{30.0300}{1.0000 0.3890 0.0821}$$

5. Step 5 — Evaluate:

   $$T = 940.3\ \text{K}$$

6. Step 6 — Check: returning T = 940.3 K to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 1,881 — kept a factor of two that cancels in the correct rearrangement.
• 470.1 — dropped that same factor in the other direction.
• 1,034 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure of solutions of electrolytes for a saline feedwater Given number of ions per molecule (Phi) = 2.0000; molar concentration (M) = 0.1530 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 274.0 K, determine the osmotic pressure (pi) in atm.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except pi is given, so isolate pi 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for pi:

   $$\pi = \Phi M R T$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 2.0000, molar concentration (M) = 0.1530 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 274.0 K.

4. Step 4 — Substitute the given values:

   $$\pi = 2.0000 0.1530 0.0821 274.0$$

5. Step 5 — Evaluate:

   $$\pi = 6.8836\ \text{atm}$$

6. Step 6 — Check: returning pi = 6.8836 atm to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 13.7672 — kept a factor of two that cancels in the correct rearrangement.
• 3.4418 — dropped that same factor in the other direction.
• 7.5720 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure calculation for an electrolyte solution in RO design Given number of ions per molecule (Phi) = 2.0000; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 301.0 K; osmotic pressure (pi) = 51.6300 atm, determine the molar concentration (M) in mol/L.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except M is given, so isolate M 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for M:

   $$M = \dfrac{\pi}{\Phi R T}$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 2.0000, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 301.0 K, osmotic pressure (pi) = 51.6300 atm.

4. Step 4 — Substitute the given values:

   $$M = \dfrac{51.6300}{2.0000 0.0821 301.0}$$

5. Step 5 — Evaluate:

   $$M = 1.0446\ \text{mol/L}$$

6. Step 6 — Check: returning M = 1.0446 mol/L to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 2.0893 — kept a factor of two that cancels in the correct rearrangement.
• 0.5223 — dropped that same factor in the other direction.
• 1.1491 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure of an electrolyte feed to a membrane system Given number of ions per molecule (Phi) = 1.0000; molar concentration (M) = 0.3350 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; osmotic pressure (pi) = 0.9400 atm, determine the absolute temperature (T) in K.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except T is given, so isolate T 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for T:

   $$T = \dfrac{\pi}{\Phi M R}$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 1.0000, molar concentration (M) = 0.3350 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, osmotic pressure (pi) = 0.9400 atm.

4. Step 4 — Substitute the given values:

   $$T = \dfrac{0.9400}{1.0000 0.3350 0.0821}$$

5. Step 5 — Evaluate:

   $$T = 34.1775\ \text{K}$$

6. Step 6 — Check: returning T = 34.1775 K to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 68.3549 — kept a factor of two that cancels in the correct rearrangement.
• 17.0887 — dropped that same factor in the other direction.
• 37.5952 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions

osmotic pressure of solutions of electrolytes for a saline feedwater Given number of ions per molecule (Phi) = 4.0000; molar concentration (M) = 0.0420 mol/L; gas constant (R) = 0.0821 L*atm/mol/K; absolute temperature (T) = 304.0 K, determine the osmotic pressure (pi) in atm.

Start with the thinking

• The governing relation printed in this handbook section is Osmotic Pressure of Solutions of Electrolytes.
• Everything except pi is given, so isolate pi 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.
• Osmotic pressure of solutions of electrolytes determines the driving pressure that must be overcome in reverse osmosis membranes.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\pi = \Phi \times M \times R \times T$$

2. Step 2 — Rearrange symbolically for pi:

   $$\pi = \Phi M R T$$

3. Step 3 — List the givens: number of ions per molecule (Phi) = 4.0000, molar concentration (M) = 0.0420 mol/L, gas constant (R) = 0.0821 L*atm/mol/K, absolute temperature (T) = 304.0 K.

4. Step 4 — Substitute the given values:

   $$\pi = 4.0000 0.0420 0.0821 304.0$$

5. Step 5 — Evaluate:

   $$\pi = 4.1930\ \text{atm}$$

6. Step 6 — Check: returning pi = 4.1930 atm to

   $$\pi = \Phi \times M \times R \times T$$

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

Why the other options are there

• 8.3860 — kept a factor of two that cancels in the correct rearrangement.
• 2.0965 — dropped that same factor in the other direction.
• 4.6123 — rounded an intermediate value before the final step.

Reference: FE Handbook — Osmotic Pressure of Electrolyte Solutions