An empty RD bottle has a mass of 25.25 g. when filled with water, the bottle has a mass
55.75 g, and 45.50 g when filled with alcohol. Find the (i) volume of the bottle, (ii) RD
Of alcohol, and (iii) density of alcohol.
Answers
Answer:
Considering:
mass of empty RD bottle: 25.25 g
mass of bottle filled with water: 55.75 g ⇒ mass of water: 55.75 - 25.25 = 30.5 g
mass of bottle filled with alcohol: 45.50 g ⇒ mass of alcohol: 45.50 - 25.25 = 20.25 g
Volume of bottle (Just for reference, you will not use it):
V=\frac{1}{3} \pi h_{2} (a^{2} +ab+b^{2} )+\pi b^{2} h_{2}V=
3
1
πh
2
(a
2
+ab+b
2
)+πb
2
h
2
aa : neck radius
bb : body radius
h_{2}h
2
: neck height
h_{1}h
1
: body height
RD = \frac{\rho Substance}{\rho Reference}RD=
ρReference
ρSubstance
Density (\rho)= \frac{Mass (m)}{Volume (V)}Density(ρ)=
Volume(V)
Mass(m)
Density of water = 1 g/mL
1 = 30.5 V1=30.5V
V = \frac{1}{30.5}mlV=
30.5
1
ml
Therefore the Volume of bottle is \frac{1}{30.5}ml
30.5
1
ml
The density of alcohol is:
DensityAlcohol (\rho)= \frac{20.25}{\frac{1}{30.5}}DensityAlcohol(ρ)=
30.5
1
20.25
DensityAlcohol (\rho)= 617.625 g/cm3DensityAlcohol(ρ)=617.625g/cm3
RDAlcohol = \frac{617.625}{1} = 617.625 g/cm3RDAlcohol=
1
617.625
=617.625g/cm3
SOLUTION:
Mass of the empty R.D bottle (m1) = 22.25 g
Mass of R.D bottle filled with water (m2) = 55.75 g
Mass of R.D bottle filled with alcohol (m3) = 45.50 g
Mass of alcohol = (m3 - m1) = (45.50 - 25.25) g
Mass of water = m2-m1 = (55.75 - 25.25) g = 30.50 g
i)
As the density of water is 1g/cm³, so the volume of water in the bottle is 30.50 cm³. This means that the volume of the bottle is 30.50 cm³.
OR
i)
Density =
➡ Volume =
➡ Volume =
iii)
R.D of Alcohol =
=
ii)
R.D of alcohol =
Density of alcohol = R.D of alcohol × density of water at 4° C
= 0.66 × 1 g/cm³ = 0.66 g/cm³
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