# Convert mole / gallon to mole / cubic inch

Learn how to convert 1 mole / gallon to mole / cubic inch step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{mole}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cubic \text{ } inch}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{mole}{cubic \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{mole}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{4.54609 \times 10^{-3}}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{4.54609 \times 10^{-3}}\left(\dfrac{mol}{m^{3}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{mole}{cubic \text{ } inch}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{1.6387064 \times 10^{-5}}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{1.6387064 \times 10^{-5}}\left(\dfrac{mol}{m^{3}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{mole}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cubic \text{ } inch}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{4.54609 \times 10^{-3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{1.6387064 \times 10^{-5}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{mole}{cubic \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{4.54609 \times 10^{-3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{mol}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{1.6387064 \times 10^{-5}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{mol}{m^{3}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{4.54609 \times 10^{-3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{1.6387064 \times 10^{-5}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{1.0}{4.54609 \times 10^{-3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.6387064 \times 10^{-5}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{4.54609 \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{1.6387064 \times {\color{rgb(99,194,222)} \cancelto{10^{-2}}{10^{-5}}}}$$
$$\text{Simplify}$$
$$\dfrac{1.0}{4.54609} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.6387064 \times 10^{-2}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.6387064 \times 10^{-2}} = \dfrac{1.0}{4.54609}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.6387064 \times 10^{-2}}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.6387064 \times 10^{-2}} \times \dfrac{1.6387064 \times 10^{-2}}{1.0} = \dfrac{1.0}{4.54609} \times \dfrac{1.6387064 \times 10^{-2}}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{1.6387064}} \times {\color{rgb(166,218,227)} \cancel{10^{-2}}}}{{\color{rgb(99,194,222)} \cancel{1.6387064}} \times {\color{rgb(166,218,227)} \cancel{10^{-2}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 1.6387064 \times 10^{-2}}{4.54609 \times {\color{rgb(255,204,153)} \cancel{1.0}}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.6387064 \times 10^{-2}}{4.54609}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0036046501\approx3.6047 \times 10^{-3}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{mole}{gallon}\right)\approx{\color{rgb(20,165,174)} 3.6047 \times 10^{-3}}\left(\dfrac{mole}{cubic \text{ } inch}\right)$$