Convert mole / cup to mole / gallon

Learn how to convert 1 mole / cup to mole / gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{m o l e}{c u p}) = x (\frac{m o l e}{g a l l o n})

Define the base values of the selected units in relation to the SI unit

(\frac{m o l e}{c u b i c m e t e r})

Left side: 1.0 (\frac{m o l e}{c u p}) = \frac{1.0}{2.365882365 \times 10^{- 4}} (\frac{m o l e}{c u b i c m e t e r}) = \frac{1.0}{2.365882365 \times 10^{- 4}} (\frac{m o l}{m^{3}})

Right side: 1.0 (\frac{m o l e}{g a l l o n}) = \frac{1.0}{4.40488377086 \times 10^{- 3}} (\frac{m o l e}{c u b i c m e t e r}) = \frac{1.0}{4.40488377086 \times 10^{- 3}} (\frac{m o l}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{m o l e}{c u p}) = x (\frac{m o l e}{g a l l o n})

Insert known values =>

1.0 \times \frac{1.0}{2.365882365 \times 10^{- 4}} \times (\frac{m o l e}{c u b i c m e t e r}) = x \times \frac{1.0}{4.40488377086 \times 10^{- 3}} \times (\frac{m o l e}{c u b i c m e t e r})

Or

1.0 \cdot \frac{1.0}{2.365882365 \times 10^{- 4}} \cdot (\frac{m o l}{m^{3}}) = x \cdot \frac{1.0}{4.40488377086 \times 10^{- 3}} \cdot (\frac{m o l}{m^{3}})

Cancel SI units

1.0 \times \frac{1.0}{2.365882365 \times 10^{- 4}} \cdot (\frac{m o l}{m^{3}}) = x \times \frac{1.0}{4.40488377086 \times 10^{- 3}} \times (\frac{m o l}{m^{3}})

Conversion Equation

\frac{1.0}{2.365882365 \times 10^{- 4}} = x \times \frac{1.0}{4.40488377086 \times 10^{- 3}}

Cancel factors on both sides

Cancel factors

\frac{1.0}{2.365882365 \times {10^{- 4}}^{10^{- 1}}} = x \times \frac{1.0}{4.40488377086 \times 10^{- 3}}

Simplify

\frac{1.0}{2.365882365 \times 10^{- 1}} = x \times \frac{1.0}{4.40488377086}

Switch sides

x \times \frac{1.0}{4.40488377086} = \frac{1.0}{2.365882365 \times 10^{- 1}}

Isolate

x

Multiply both sides by

(\frac{4.40488377086}{1.0})

x \times \frac{1.0}{4.40488377086} \times \frac{4.40488377086}{1.0} = \frac{1.0}{2.365882365 \times 10^{- 1}} \times \frac{4.40488377086}{1.0}

Cancel

x \times \frac{1.0 \times 4.40488377086}{4.40488377086 \times 1.0} = \frac{1.0 \times 4.40488377086}{2.365882365 \times 10^{- 1} \times 1.0}

Simplify

x = \frac{4.40488377086}{2.365882365 \times 10^{- 1}}

Rewrite equation

\frac{1.0}{10^{- 1}} can be rewritten to 10

Rewrite

x = \frac{10.0 \times 4.40488377086}{2.365882365}

Solve

x

x \approx 18.618354978 \approx 18.6184

Conversion Equation

1.0 (\frac{m o l e}{c u p}) \approx 18.6184 (\frac{m o l e}{g a l l o n})

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