Convert mole / gallon to mole / cubic foot
Learn how to convert
1
mole / gallon to
mole / cubic foot
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mole}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cubic \text{ } foot}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{mole}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mole}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{4.40488377086 \times 10^{-3}}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{4.40488377086 \times 10^{-3}}\left(\dfrac{mol}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{mole}{cubic \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{0.028316846592}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{0.028316846592}\left(\dfrac{mol}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mole}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cubic \text{ } foot}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{4.40488377086 \times 10^{-3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{0.028316846592}}} \times {\color{rgb(125,164,120)} \left(\dfrac{mole}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{4.40488377086 \times 10^{-3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{mol}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{0.028316846592}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{mol}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{4.40488377086 \times 10^{-3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{0.028316846592}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{4.40488377086 \times 10^{-3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{0.028316846592}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{4.40488377086 \times 10^{-3}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{0.028316846592}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{0.028316846592} = \dfrac{1.0}{4.40488377086 \times 10^{-3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{0.028316846592}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{0.028316846592} \times \dfrac{0.028316846592}{1.0} = \dfrac{1.0}{4.40488377086 \times 10^{-3}} \times \dfrac{0.028316846592}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{0.028316846592}}}{{\color{rgb(99,194,222)} \cancel{0.028316846592}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 0.028316846592}{4.40488377086 \times 10^{-3} \times {\color{rgb(255,204,153)} \cancel{1.0}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.028316846592}{4.40488377086 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 0.028316846592}{4.40488377086}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx6.4285116396\approx6.4285\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mole}{gallon}\right)\approx{\color{rgb(20,165,174)} 6.4285}\left(\dfrac{mole}{cubic \text{ } foot}\right)\)
