Changing the Subject of Formula

Changing the Subject of a Formula

Very often in science you will have to change the subject of a formula. We will look at two examples. (Do not worry if you do not yet know what the terms and symbols mean, these formulae will be covered later.)

Moles

The equation to calculate moles from molar mass is: \(n=\dfrac{m}{M}\), where \(n\) is the number of moles, \(m\) is the mass and \(M\) is the molar mass. As it is written we can easily find the number of moles of a substance. But what if we have the number of moles and want to find the molar mass? We note that we can simply multiply both sides of the equation by the molar mass and then divide both sides by the number of moles.

\begin{align*} n& = \frac{m}{M} \\ nM & = m \\ M & = \frac{m}{n} \end{align*}

And if we wanted the mass we would use: \(m=nM\).

Energy of a Photon

The equation for the energy of a photon is \(E=h\dfrac{c}{\lambda }\), where \(E\) is the energy, \(h\) is Planck's constant, \(c\) is the speed of light and \(\lambda\) is the wavelength. To get \(c\) we can do the following:

\begin{align*} E & = h\frac{c}{\lambda } \\ E\lambda & = hc \\ c & = \frac{E\lambda }{h} \end{align*}

Similarly we can find the wavelength we use: \(\lambda =\dfrac{hc}{E}\) and to find Planck's constant we use: \(h=\dfrac{E\lambda }{c}\).