Answer:
[tex]\alpha=6.022*10^{20}\frac{m^3 * molecules}{L * mol}[/tex]
Explanation:
Hi, the question states that there is a proportional relation between m (molarity) and n (number density), by following formula:
[tex]m=\alpha*n[/tex]
The units of alpha ([tex]\alpha[/tex]) 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: [tex]1 m^3=1000 L[/tex]
2) We also need to find a relation between mol and molecules. The relation is given by the Avogadro's number: [tex]A=6.022*10^{23} \frac{molecules}{mol}[/tex]
With this two numbers we can balance the units and find the value of [tex]\alpha[/tex] :
[tex]\alpha=\frac{1 m^3}{1000 L}*6.022*10^{23}\frac{molecules}{mol}[/tex]
[tex]\alpha=6.022*10^{20}\frac{m^3 * molecules}{L * mol}[/tex]
