Question

"To determine the amount of heroin in the mixture, you dissolve 1.00 g of the white powdery mixture in water in a 100.0-mL volumetric flask. You find that the solution has an osmotic pressure of 531 mm Hg at 25 °C. What is the composition of the mixture?"

Answer 1

Step-by-step explanation:

Formula to calculate osmotic pressure is as follows.

Osmotic pressure = concentration × gas constant × temperature( in K)

Temperature =
`25^(o) C`

= (25 + 273) K

= 298.15 K

Osmotic pressure = 531 mm Hg or 0.698 atm (as 1 mm Hg = 0.00131)

Putting the given values into the above formula as follows.

0.698 =
`C * 0.082 * 298.15 K`

C = 0.0285

This also means that,

`\frac{\text{moles}}{\text{volume (in L)}}` = 0.0285

So, moles = 0.0285 × volume (in L)

= 0.0285 × 0.100

=
`2.85 * 10^(-3 )`

Now, let us assume that mass of
`C_(12)H_(23)O_(5)N` = x grams

And, mass of
`C_(12)H{22}O_(11)` = (1.00 - x)

So, moles of
`C_(12)H_(23)O_(5)N = \frac{mass}{\text{molar mass}}`

=
`(x)/(369)`

Now, moles of
`C_(12)H_(22)O_(11) = ((1.00 - x))/(342)`

=
`(x)/(369) + ((1.00 - x))/(342)`

=
`2.85 * 10^(-3)`

= x = 0.346

Therefore, we can conclude that amount of
`C_(12)H_(23)O_(5)N` present is 0.346 g and amount of
`C_(12)H_(22)O_(11)` present is (1 - 0.346) g = 0.654 g.