Convert mole / (acre • foot) to mole / cup
Learn how to convert
1
mole / (acre • foot) to
mole / cup
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mole}{acre \times foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cup}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{mole}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mole}{acre \times foot}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1233.48183754752}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1233.48183754752}\left(\dfrac{mol}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{mole}{cup}\right) = {\color{rgb(125,164,120)} 4.0 \times 10^{3}\left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 4.0 \times 10^{3}\left(\dfrac{mol}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mole}{acre \times foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mole}{cup}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1233.48183754752}} \times {\color{rgb(89,182,91)} \left(\dfrac{mole}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4.0 \times 10^{3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{mole}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1233.48183754752}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{mol}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4.0 \times 10^{3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{mol}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1233.48183754752}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4.0 \times 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{mol}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{1233.48183754752} = {\color{rgb(20,165,174)} x} \times 4.0 \times 10^{3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 4.0 \times 10^{3} = \dfrac{1.0}{1233.48183754752}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{4.0 \times 10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 4.0 \times 10^{3} \times \dfrac{1.0}{4.0 \times 10^{3}} = \dfrac{1.0}{1233.48183754752} \times \dfrac{1.0}{4.0 \times 10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4.0}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4.0}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = \dfrac{1.0 \times 1.0}{1233.48183754752 \times 4.0 \times 10^{3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{1233.48183754752 \times 4.0 \times 10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3}}{1233.48183754752 \times 4.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000002027\approx2.0268 \times 10^{-7}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mole}{acre \times foot}\right)\approx{\color{rgb(20,165,174)} 2.0268 \times 10^{-7}}\left(\dfrac{mole}{cup}\right)\)
