Convert mole / cubic inch to mole / cup

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

Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{mole}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cup}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{mole}{cubic \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{mole}{cubic \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-5}}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-5}}\left(\dfrac{mol}{m^{3}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{mole}{cup}\right) = {\color{rgb(125,164,120)} 4.0 \times 10^{3}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 4.0 \times 10^{3}\left(\dfrac{mol}{m^{3}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{mole}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cup}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4.0 \times 10^{3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{mole}{cubic \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{mol}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4.0 \times 10^{3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{mol}{m^{3}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4.0 \times 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{1.0}{1.6387064 \times 10^{-5}} = {\color{rgb(20,165,174)} x} \times 4.0 \times 10^{3}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 4.0 \times 10^{3} = \dfrac{1.0}{1.6387064 \times 10^{-5}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{4.0 \times 10^{3}}\right)$$
$${\color{rgb(20,165,174)} x} \times 4.0 \times 10^{3} \times \dfrac{1.0}{4.0 \times 10^{3}} = \dfrac{1.0}{1.6387064 \times 10^{-5}} \times \dfrac{1.0}{4.0 \times 10^{3}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4.0}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4.0}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = \dfrac{1.0 \times 1.0}{1.6387064 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}} \times 4.0 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.6387064 \times 10^{-2} \times 4.0}$$
Rewrite equation
$$\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{2}}{1.6387064 \times 4.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx15.255936024\approx15.2559$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{mole}{cubic \text{ } inch}\right)\approx{\color{rgb(20,165,174)} 15.2559}\left(\dfrac{mole}{cup}\right)$$