Question

In a tank of water, a can of regular soda will sink to the bottom, but a can of diet soda will float.

In a regular soda, about 25 cm^3 of sugar is dissolved in 12 oz of carbonated water. The density of table sugar is 1.6 g/cm^3

In a diet soda, about 0.2 cm^3 of aspartame (artificial sweetener) is dissolved in 12 oz of carbonated water. The density of aspartame is 1.35 g/cm^3

How many times as great is the mass of the sugar in regular soda as the mass of the sweetener in diet soda?
Please choose from one of the following options.

Answer 1

Over 140 times bigger because 25 cm³ of sugar is 40 grams (25×1.6)
and .2 cm³ of aspartame is 0.27 grams (0.2×1.35)
and 40 is 148 times as big as 0.27 (0.27×148.1481481≈40)

Answer 2

Over 140 times as great the mass of the sugar in regular soda as the mass of the sweetener in diet soda.

Explanation:

In Regular Soda

Volume of sugar =
`25 cm^3`

Density of table sugar =
`1.6 g/cm^3`

`mass = volume * density`

So, Mass of Sugar in regular soda =
`25 * 1.6`

=
`40 g`

In Diet Soda

Volume of aspartame =
`0.2 cm^3`

Density of aspartame =
`1.35 g/cm^3`

`mass = volume * density`

So, Mass of aspartame in diet soda =
`0.2 * 1.35`

=
`0.27 g`

So, now to find How many times as great is the mass of the sugar in regular soda as the mass of the sweetener in diet soda:

`\frac{\text{Mass of Sugar}}{\text{mass of aspartame}}`

`(40)/(0.27)`

`148.1481`

Hence Over 140 times as great the mass of the sugar in regular soda as the mass of the sweetener in diet soda.

Thus Option D is correct.