Question

Gasoline and kerosene (specific gravity 0.820) are blended to obtain a mixture with a specific gravity of 0.770. Calculate the volumetric ratio (volume of gasoline/volume of kerosene) of the two compounds in the mixture, assuming Vblend = Vgasoline + Vkerosene.

Answer 1

Answer:

The volumetric ratio is 0,71

Explanation:

Let's begin with the equation:

$Db = Mb/Vb$ (1)

Where:

Db: Blend Density, Mb: Blend Mass and Vb: Blend Volume

And we know: $Vb = Vg + Vk$ (2)

Where:

Vg: Gasoline Volume and Vk: Kerosene Volume

Therefore replacing (2) into (1):

$Db = (Mg + Mk) / (Vg + Vk)$

$Db = (Dg * Vg + Dk * Vk)/(Vg + Vk)$ (3)

Where:

Dg: Gasoline Density and Dk: Kerosene Density

The specific gravity is defined as:

$SG = Substance Density / Reference Density$

Therefore:

$Db = SGb * Dref\\Dg = SGg * Dref\\Dk = SGk * Dref$

Where:

Dref: Reference Density

SGb: Blend Specific Gravity

SGg: Gasoline Specific Gravity (which is 0.7 approximately)

SGk: Kerosene Specific Gravity

Replacing these equations into (3) we get:

$SGb * Dref = (SGg * Dref * Vg + SGk * Dref * Vk)/(Vg + Vk)$

$SGb * Dref = Dref * (SGg * Vg + SGk * Vk)/(Vg + Vk)$

$SGb = (SGg * Vg + SGk * Vk)/(Vg + Vk)$

$SGb * (Vg + Vk) = SGg * Vg + SGk * Vk$

$SGb * Vg + SGb* Vk = SGg * Vg + SGk * Vk$

Replacing with the Specific Gravity data, we obtain:

$0.77 * Vg + 0.77 * Vk = 0.7 * Vg + 0.82 * Vk$

$0.77 * Vg - 0.7 * Vg = 0.82 * Vk - 0.77 * Vk$

$0.07 * Vg = 0.05 * Vk$

$Vg/Vk = 0.05/0.07$

$Vg/Vk = 0.71$