Question

Calculate the molar mass of the artificial sweetener?

A low carbohydrate recipe for ice cream uses an artificial sweetener instead of sugar but doesn't name the sweetener. To determine the identity of the sweetener, the osmotic pressure of a solution was measured at 7.2 atm. The ice cream solution was prepared at 298 degrees kelvin by adding 82.5 grams of sweetener to make .71 L of solution.

Answer 1

Recall,

`Pi = iMRT`

Let's first derive the molarity of the synthetic sweetener (assuming `i = 1`),

`"7.2 atm" = 1 cdot M cdot ("0.08206 L"cdot"atm")/("mol" cdot "K") cdot "298 K"`

`therefore M approx "0.294 M"`

Hence,

`("82.5 g" * 1/M "mol"/"g")/("0.71 L") = "0.294 M"`

`therefore M approx "395 g/mol"`

is the approximate molar mass of the synthetic sugar under investigation, given your data.