Convert mole / barrel to mole / cup

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

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Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{mole}{barrel}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cup}\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{mole}{cubic \text{ } meter}\right)\)

\(\text{Left side: 1.0 } \left(\dfrac{mole}{barrel}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{0.16365924}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{0.16365924}\left(\dfrac{mol}{m^{3}}\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{mole}{cup}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{2.365882365 \times 10^{-4}}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{2.365882365 \times 10^{-4}}\left(\dfrac{mol}{m^{3}}\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(\dfrac{mole}{barrel}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cup}\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{0.16365924}} \times {\color{rgb(89,182,91)} \left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{2.365882365 \times 10^{-4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{mole}{cubic \text{ } meter}\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{0.16365924}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{mol}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{2.365882365 \times 10^{-4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{mol}{m^{3}}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{0.16365924}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{2.365882365 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{1.0}{0.16365924} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.365882365 \times 10^{-4}}\)

Cancel factors on both sides

\(\text{Cancel factors}\)

\(\dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{0.16365924} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{2.365882365 \times 10^{-4}}\)

Switch sides

\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.365882365 \times 10^{-4}} = \dfrac{1.0}{0.16365924}\)

Isolate \({\color{rgb(20,165,174)} x}\)

Multiply both sides by \(\left(\dfrac{2.365882365 \times 10^{-4}}{1.0}\right)\)

\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.365882365 \times 10^{-4}} \times \dfrac{2.365882365 \times 10^{-4}}{1.0} = \dfrac{1.0}{0.16365924} \times \dfrac{2.365882365 \times 10^{-4}}{1.0}\)

\(\text{Cancel}\)

\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{2.365882365}} \times {\color{rgb(166,218,227)} \cancel{10^{-4}}}}{{\color{rgb(99,194,222)} \cancel{2.365882365}} \times {\color{rgb(166,218,227)} \cancel{10^{-4}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 2.365882365 \times 10^{-4}}{0.16365924 \times {\color{rgb(255,204,153)} \cancel{1.0}}}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{2.365882365 \times 10^{-4}}{0.16365924}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx0.0014456149\approx1.4456 \times 10^{-3}\)

\(\text{Conversion Equation}\)

\(1.0\left(\dfrac{mole}{barrel}\right)\approx{\color{rgb(20,165,174)} 1.4456 \times 10^{-3}}\left(\dfrac{mole}{cup}\right)\)