retardation factor of a sorbing contaminant plume in an aquifer Given bulk density (rho_b) = 1.5200 g/cm^3; distribution coefficient (K_d) = 8.5300 cm^3/g; porosity (n) = 0.2400, determine the retardation factor (R).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except R is given, so isolate R 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for R:

   $$R = 1+\dfrac{\rho_b K_d}{n}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.5200 g/cm^3, distribution coefficient (K_d) = 8.5300 cm^3/g, porosity (n) = 0.2400.

4. Step 4 — Substitute the given values:

   $$R = 1+\dfrac{\rho_b K_d}{0.2400}$$

5. Step 5 — Evaluate:

   $$R = 55.0233$$

6. Step 6 — Check: returning R = 55.0233 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 110.0 — kept a factor of two that cancels in the correct rearrangement.
• 27.5117 — dropped that same factor in the other direction.
• 60.5257 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor R calculation from bulk density, distribution coefficient, and porosity Given bulk density (rho_b) = 1.7500 g/cm^3; porosity (n) = 0.3700; retardation factor (R) = 15.3000, determine the distribution coefficient (K_d) in cm^3/g.

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except K_d is given, so isolate K_d 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for K_d:

   $$K_{d} = \dfrac{(R-1)n}{\rho_b}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.7500 g/cm^3, porosity (n) = 0.3700, retardation factor (R) = 15.3000.

4. Step 4 — Substitute the given values:

   $$K_{d} = \dfrac{(15.3000-1)0.3700}{\rho_b}$$

5. Step 5 — Evaluate:

   K_{d} = 3.0234\ \text{cm^3/g}

6. Step 6 — Check: returning K_d = 3.0234 cm^3/g to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 6.0469 — kept a factor of two that cancels in the correct rearrangement.
• 1.5117 — dropped that same factor in the other direction.
• 3.3258 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor used to estimate contaminant travel time in groundwater Given bulk density (rho_b) = 1.7900 g/cm^3; distribution coefficient (K_d) = 2.5700 cm^3/g; retardation factor (R) = 27.4000, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except n is given, so isolate n 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for n:

   $$n = \dfrac{\rho_b K_d}{R-1}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.7900 g/cm^3, distribution coefficient (K_d) = 2.5700 cm^3/g, retardation factor (R) = 27.4000.

4. Step 4 — Substitute the given values:

   $$n = \dfrac{\rho_b K_d}{27.4000-1}$$

5. Step 5 — Evaluate:

   $$n = 0.1743$$

6. Step 6 — Check: returning n = 0.1743 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 0.3485 — kept a factor of two that cancels in the correct rearrangement.
• 0.0871 — dropped that same factor in the other direction.
• 0.1917 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor of a sorbing contaminant plume in an aquifer Given bulk density (rho_b) = 1.3800 g/cm^3; distribution coefficient (K_d) = 4.5800 cm^3/g; porosity (n) = 0.4000, determine the retardation factor (R).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except R is given, so isolate R 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for R:

   $$R = 1+\dfrac{\rho_b K_d}{n}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.3800 g/cm^3, distribution coefficient (K_d) = 4.5800 cm^3/g, porosity (n) = 0.4000.

4. Step 4 — Substitute the given values:

   $$R = 1+\dfrac{\rho_b K_d}{0.4000}$$

5. Step 5 — Evaluate:

   $$R = 16.8010$$

6. Step 6 — Check: returning R = 16.8010 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 33.6020 — kept a factor of two that cancels in the correct rearrangement.
• 8.4005 — dropped that same factor in the other direction.
• 18.4811 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor R calculation from bulk density, distribution coefficient, and porosity Given bulk density (rho_b) = 1.8500 g/cm^3; porosity (n) = 0.3800; retardation factor (R) = 12.2000, determine the distribution coefficient (K_d) in cm^3/g.

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except K_d is given, so isolate K_d 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for K_d:

   $$K_{d} = \dfrac{(R-1)n}{\rho_b}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.8500 g/cm^3, porosity (n) = 0.3800, retardation factor (R) = 12.2000.

4. Step 4 — Substitute the given values:

   $$K_{d} = \dfrac{(12.2000-1)0.3800}{\rho_b}$$

5. Step 5 — Evaluate:

   K_{d} = 2.3005\ \text{cm^3/g}

6. Step 6 — Check: returning K_d = 2.3005 cm^3/g to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 4.6011 — kept a factor of two that cancels in the correct rearrangement.
• 1.1503 — dropped that same factor in the other direction.
• 2.5306 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor used to estimate contaminant travel time in groundwater Given bulk density (rho_b) = 1.6900 g/cm^3; distribution coefficient (K_d) = 2.9500 cm^3/g; retardation factor (R) = 32.2000, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except n is given, so isolate n 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for n:

   $$n = \dfrac{\rho_b K_d}{R-1}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.6900 g/cm^3, distribution coefficient (K_d) = 2.9500 cm^3/g, retardation factor (R) = 32.2000.

4. Step 4 — Substitute the given values:

   $$n = \dfrac{\rho_b K_d}{32.2000-1}$$

5. Step 5 — Evaluate:

   $$n = 0.1598$$

6. Step 6 — Check: returning n = 0.1598 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 0.3196 — kept a factor of two that cancels in the correct rearrangement.
• 0.0799 — dropped that same factor in the other direction.
• 0.1758 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor of a sorbing contaminant plume in an aquifer Given bulk density (rho_b) = 1.7100 g/cm^3; distribution coefficient (K_d) = 6.3700 cm^3/g; porosity (n) = 0.3000, determine the retardation factor (R).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except R is given, so isolate R 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for R:

   $$R = 1+\dfrac{\rho_b K_d}{n}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.7100 g/cm^3, distribution coefficient (K_d) = 6.3700 cm^3/g, porosity (n) = 0.3000.

4. Step 4 — Substitute the given values:

   $$R = 1+\dfrac{\rho_b K_d}{0.3000}$$

5. Step 5 — Evaluate:

   $$R = 37.3090$$

6. Step 6 — Check: returning R = 37.3090 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 74.6180 — kept a factor of two that cancels in the correct rearrangement.
• 18.6545 — dropped that same factor in the other direction.
• 41.0399 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor R calculation from bulk density, distribution coefficient, and porosity Given bulk density (rho_b) = 1.6900 g/cm^3; porosity (n) = 0.2900; retardation factor (R) = 20.5000, determine the distribution coefficient (K_d) in cm^3/g.

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except K_d is given, so isolate K_d 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for K_d:

   $$K_{d} = \dfrac{(R-1)n}{\rho_b}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.6900 g/cm^3, porosity (n) = 0.2900, retardation factor (R) = 20.5000.

4. Step 4 — Substitute the given values:

   $$K_{d} = \dfrac{(20.5000-1)0.2900}{\rho_b}$$

5. Step 5 — Evaluate:

   K_{d} = 3.3462\ \text{cm^3/g}

6. Step 6 — Check: returning K_d = 3.3462 cm^3/g to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 6.6923 — kept a factor of two that cancels in the correct rearrangement.
• 1.6731 — dropped that same factor in the other direction.
• 3.6808 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor used to estimate contaminant travel time in groundwater Given bulk density (rho_b) = 1.5700 g/cm^3; distribution coefficient (K_d) = 7.7900 cm^3/g; retardation factor (R) = 2.5000, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except n is given, so isolate n 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for n:

   $$n = \dfrac{\rho_b K_d}{R-1}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.5700 g/cm^3, distribution coefficient (K_d) = 7.7900 cm^3/g, retardation factor (R) = 2.5000.

4. Step 4 — Substitute the given values:

   $$n = \dfrac{\rho_b K_d}{2.5000-1}$$

5. Step 5 — Evaluate:

   $$n = 8.1535$$

6. Step 6 — Check: returning n = 8.1535 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 16.3071 — kept a factor of two that cancels in the correct rearrangement.
• 4.0768 — dropped that same factor in the other direction.
• 8.9689 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor

retardation factor of a sorbing contaminant plume in an aquifer Given bulk density (rho_b) = 1.5100 g/cm^3; distribution coefficient (K_d) = 2.7800 cm^3/g; porosity (n) = 0.2100, determine the retardation factor (R).

Start with the thinking

• The governing relation printed in this handbook section is Retardation Factor R.
• Everything except R is given, so isolate R 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.
• The retardation factor R describes how much slower a sorbing contaminant moves relative to groundwater seepage velocity.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

2. Step 2 — Rearrange symbolically for R:

   $$R = 1+\dfrac{\rho_b K_d}{n}$$

3. Step 3 — List the givens: bulk density (rho_b) = 1.5100 g/cm^3, distribution coefficient (K_d) = 2.7800 cm^3/g, porosity (n) = 0.2100.

4. Step 4 — Substitute the given values:

   $$R = 1+\dfrac{\rho_b K_d}{0.2100}$$

5. Step 5 — Evaluate:

   $$R = 20.9895$$

6. Step 6 — Check: returning R = 20.9895 to

   $$R = 1 + \dfrac{\rho_b K_d}{n}$$

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

Why the other options are there

• 41.9790 — kept a factor of two that cancels in the correct rearrangement.
• 10.4948 — dropped that same factor in the other direction.
• 23.0885 — rounded an intermediate value before the final step.

Reference: FE Handbook — Retardation Factor