# 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
$$1.0\left(\dfrac{mole}{cup}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{gallon}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{mole}{cubic \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{mole}{cup}\right) = {\color{rgb(89,182,91)} 4.0 \times 10^{3}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 4.0 \times 10^{3}\left(\dfrac{mol}{m^{3}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{mole}{gallon}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{3.785411784 \times 10^{-3}}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{3.785411784 \times 10^{-3}}\left(\dfrac{mol}{m^{3}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{mole}{cup}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{gallon}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 4.0 \times 10^{3}} \times {\color{rgb(89,182,91)} \left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{3.785411784 \times 10^{-3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{mole}{cubic \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 4.0 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{mol}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{3.785411784 \times 10^{-3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{mol}{m^{3}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 4.0 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{3.785411784 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}}$$
$$\text{Conversion Equation}$$
$$4.0 \times 10^{3} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.785411784 \times 10^{-3}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.785411784 \times 10^{-3}} = 4.0 \times 10^{3}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{3.785411784 \times 10^{-3}}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.785411784 \times 10^{-3}} \times \dfrac{3.785411784 \times 10^{-3}}{1.0} = 4.0 \times 10^{3} \times \dfrac{3.785411784 \times 10^{-3}}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{3.785411784}} \times {\color{rgb(166,218,227)} \cancel{10^{-3}}}}{{\color{rgb(99,194,222)} \cancel{3.785411784}} \times {\color{rgb(166,218,227)} \cancel{10^{-3}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = 4.0 \times {\color{rgb(255,204,153)} \cancel{10^{3}}} \times \dfrac{3.785411784 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}}{1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = 4.0 \times 3.785411784$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 15.141647136\approx15.1416$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{mole}{cup}\right)\approx{\color{rgb(20,165,174)} 15.1416}\left(\dfrac{mole}{gallon}\right)$$