Answer:
The correct answers are:
a) 180 g
b) 93.7 cm³
Explanation:
The density of a substance is the mass of the substance per unit of volume. So, it is calculated as follows:
density= mass/volume
From the data provided in the problem:
density = 0.8 g/cm³
a) Given: volume= 225 cm³
mass= density x volume = 0.8 g/cm³ x 225 cm³ = 180 g
b) Given: mass= 75.0 g
volume = mass/density = 75.0 g/(0.8 g/cm³)= 93.75 cm³≅ 93.7 cm³
Taking into account the definition of density:
Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.
In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance. Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
[tex]density=\frac{mass}{volume} [/tex]
From this expression it can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.
In this case, you know that:
Replacing in the definition of density:
[tex]0.8 \frac{g}{cm^{3} } =\frac{mass}{225 cm^{3} } [/tex]
Solving:
mass= 0.8 [tex]\frac{g}{cm^{3} } [/tex] ×225 cm³
mass= 180 g
In summary, the mass of 225 cm³ of ethanol is 180 g.
In this case, you know that:
Replacing in the definition of density:
[tex]0.8 \frac{g}{cm^{3} } =\frac{75 g}{volume} [/tex]
Solving:
0.8 [tex]\frac{g}{cm^{3} } [/tex] ×volume= 75 g
volume= 75 g÷ 0.8 [tex]\frac{g}{cm^{3} } [/tex]
volume= 93.75 cm³
Finally, the volume of 75.0 g of ethanol is 93.75 cm³.
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