Question

Consider a mixture of NaCl and NaNO3 that is 31.8% Na by mass. Calculate the percentage by mass of NaCl in the mixture.

Answer 1

Answer: The percentage by mass of NaCl in the mixture is 38.5 %

Step-by-step explanation:

To calculate the mass percentage of element in compound, we use the equation:

`\text{Mass percent of element}=\frac{\text{Mass of element}}{\text{Mass of compound}}* 100` .......(1)

• For NaCl:

Mass of sodium element = 23 g

Mass of NaCl = 58.5 g

Putting values in equation 1, we get:

`\text{Mass percent of sodium element}=(23g)/(58.5g)* 100=39.32\%`

Mass fraction of sodium metal in NaCl = 0.3932

• For
  `NaNO_3` :

Mass of sodium element = 23 g

Mass of
`NaNO_3` = 85 g

Putting values in equation 1, we get:

`\text{Mass percent of sodium element}=(23g)/(85g)* 100=27.1\%`

Mass fraction of sodium metal in sodium nitrate = 0.271

Let us assume the mass fraction of NaCl in the mixture is 'x'

So, the mass fraction of
`NaNO_3` in the mixture will be '(1-x)'

We are given:

Percent by mass of Na in the mixture = 31.8 %

Mass fraction of Na in the mixture = 0.318

Evaluating the mass fraction of NaCl in the mixture:

`[(x* 0.3932)+((1-x)* 0.271)]=0.318`

x = 0.385

Percent by mass of NaCl in the mixture will be =
`(0.385* 100)=38.5\%`

Hence, the percentage by mass of NaCl in the mixture is 38.5 %