Question

A sample of vinaigrette salad dressing has a total mass of 188 g

188 g , a total volume of 196 cm

3

196⁢ cm3 , and consists only of oil (density=0.882 g/cm

3

)

(density=0.882⁢ g/cm3) and vinegar (density=1.056 g/cm

3

)

(density=1.056⁢ g/cm3) .

What is the volume of each component in this mixture? Assume that the volumes are additive.

Answer 1

$m=188g, v=196cm^3,density_1=0.882g/cm^3,density_2=1.056g/cm^3$

$v_1=?, v_2=?$

$v=m_1/density_1+m_2/density_2=196$

$m=m_1+m_2=188, m_1=188-m_2$

$m_1/0.882+m_2/1.056=196$

$1.056m_1+0.882m_2=196\times 0.882\times 1.056$

$1.056(188-m_2)+0.882m_2=182.553$

$198.528-1.056m_2+0.882m_2=182.553$

$15.975=0.174m_2$

$m_2=91.81g$

$v_2=m_2/density_2=91.81/1.056=86.94cm^3$

$v_1=196-86.94=109.06cm^3$

volume of oil=$109.06cm^3$

volume of vinegar=$86.94cm^3$