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Question: A mass of mercury occupies \( 0.95{\text{ L}} \) . What volume would an equal mass of ethanol occupy...

A mass of mercury occupies 0.95 L0.95{\text{ L}} . What volume would an equal mass of ethanol occupy? The density of mercury is 13.546 g mL−1{\text{13}}{\text{.546 g m}}{{\text{L}}^{ - 1}} and the density of ethanol is 0.789 g mL−1{\text{0}}{\text{.789 g m}}{{\text{L}}^{ - 1}} ?

Explanation

Solution

Since we are given the density of mercury, we will find the mass of mercury in 0.95 L0.95{\text{ L}} . The mass of mercury which is present in 0.95 L0.95{\text{ L}} of mercury will be used to find the volume of ethanol having density equals to 0.789 g mL−1{\text{0}}{\text{.789 g m}}{{\text{L}}^{ - 1}} . We will convert all volume in millilitres since the density is given as g mL−1{\text{g m}}{{\text{L}}^{ - 1}} .

Complete Step By Step Answer:
Step (i)(i) : To calculate the mass of mercury in 0.95 L0.95{\text{ L}}
The density of mercury is given as: 13.546 g mL−1{\text{13}}{\text{.546 g m}}{{\text{L}}^{ - 1}} . Density of any substance is the ratio of mass of substance and its volume. Before finding the mass of substance we will convert all volume units into millilitre. We will use the following conversion factor:
⇒ 1L = 1000 mL\Rightarrow {\text{ 1L = 1000 mL}}
⇒ 1 mL = 10−3 L\Rightarrow {\text{ 1 mL = 1}}{{\text{0}}^{ - 3}}{\text{ L}}
The density of any substance can be represented as:
⇒ Density = massvolume\Rightarrow {\text{ Density = }}\dfrac{{mass}}{{volume}}
⇒ mass = density × volume\Rightarrow {\text{ mass = density }} \times {\text{ volume}}
For mercury it can be represented as:
⇒ mass = 13.546 g mL−1 × 0.95 L\Rightarrow {\text{ mass = 13}}{\text{.546 g m}}{{\text{L}}^{ - 1}}{\text{ }} \times {\text{ 0}}{\text{.95 L}}
After converting litre into millilitres it can be shown as:
⇒ mass = 13.546 g mL−1 × 0.95 × 1000 mL\Rightarrow {\text{ mass = 13}}{\text{.546 g m}}{{\text{L}}^{ - 1}}{\text{ }} \times {\text{ 0}}{\text{.95 }} \times {\text{ 1000 mL}}
⇒ mass = 12868.7 g\Rightarrow {\text{ mass = 12868}}{\text{.7 g}}
Step (ii)(ii) : To calculate volume of ethanol
Now the above calculated mass will be used in finding the volume of ethanol used having density equal to 0.789 g mL−1{\text{0}}{\text{.789 g m}}{{\text{L}}^{ - 1}} . Since we know that,
⇒ Density = massvolume\Rightarrow {\text{ Density = }}\dfrac{{mass}}{{volume}}
⇒ Volume = massdensity\Rightarrow {\text{ Volume = }}\dfrac{{mass}}{{density}}
⇒ Volume = 12868.7 g0.789 g mL−1\Rightarrow {\text{ Volume = }}\dfrac{{{\text{12868}}{\text{.7 g}}}}{{{\text{0}}{\text{.789 g m}}{{\text{L}}^{ - 1}}}}
⇒ Volume = 12868.7 g0.789 g mL−1\Rightarrow {\text{ Volume = }}\dfrac{{{\text{12868}}{\text{.7 g}}}}{{{\text{0}}{\text{.789 g m}}{{\text{L}}^{ - 1}}}}
⇒ Volume = 16310.13 mL\Rightarrow {\text{ Volume = 16310}}{\text{.13 mL}}
In litres it can be converted as:
⇒ Volume = 16 L\Rightarrow {\text{ Volume = 16 L}}
Hence the volume of ethanol will be equal to 16 L{\text{16 L}} which would have same mass of 0.95 L0.95{\text{ L}} of mercury which have density equals to 13.546 g mL−1{\text{13}}{\text{.546 g m}}{{\text{L}}^{ - 1}} .

Note:
All the volumetric units must be in the same standard whether millilitres or litres. We can also convert density of solution in terms of litre but for easy calculation we convert the given volumes of solution. At last we get a volume of ethanol in millilitres which can be converted into litres by dividing by a factor of 10001000 .