Question

Let's write that m = molarity in units of moles/liter and n = number density = N/V, the number of molecules divided by the volume they are in, in units of molecules/m3. Since m and n must be proportional, we expect there is an equation n = αm where α is some constant. Find the numerical value of α and its units (keeping "moles" and "molecules" as units).

Answer 1

Answer:

$\alpha=6.022*10^{20}\frac{m^3 * molecules}{L * mol}$

Explanation:

Hi, the question states that there is a proportional relation between m (molarity) and n (number density), by following formula:

$m=\alpha*n$

The units of alpha ($\alpha$) must help to balance the units of m and n.  

1) First in both sides there are volume units liter and m3. So we need to express all volume in the same unit. Knowing that: $1 m^3=1000 L$

2) We also need to find a relation between mol and molecules. The relation is given by the Avogadro's number: $A=6.022*10^{23} \frac{molecules}{mol}$

With this two numbers we can balance the units and find the value of $\alpha$ :

$\alpha=\frac{1 m^3}{1000 L}*6.022*10^{23}\frac{molecules}{mol}$

$\alpha=6.022*10^{20}\frac{m^3 * molecules}{L * mol}$