What is the volume of 100 moles of mercury? Two ways to solve the problem

2024 Author: Angel Austin | [email protected]. Last modified: 2023-12-17 05:14

A typical task in physics is to calculate the volumes of various substances under certain external conditions. One of these substances is mercury - a metal with unique physical properties. In this article, we will consider ways to solve the following task in physics: what is the volume of 100 moles of mercury?

What is mercury?

This is a chemical element under the 80th number in the periodic table. Its neighbor on the left is gold. Mercury is denoted by the symbol Hg (hydrargyrum). The Latin name can be translated as "liquid silver". Indeed, at room temperature, the element exists as a liquid, which has a silvery color.

The element in question is the only liquid metal. This fact is due to the unique electronic structure of its atoms. It is extremely stable due to fully filled electron shells. In this regard, mercury is similar to inert gases. Atom stabilityleads to the difficulty of detaching an electron from it. The latter means that there is no metallic bond between Hg atoms, they interact with each other only due to weak van der Waals forces.

Mercury already melts at -39 ^oC. The resulting liquid is very heavy. Its density is 13,546 kg/m^{3, which is 13.5 times that of distilled water. This density value is due to the large value of the atomic mass of the element, which is 200.59 a.m.u.}

Further in the article, we will answer the question of how much volume is occupied by 100 moles of mercury. This problem can be solved in two different ways.

Solution of the problem in the first way

To answer the question: "What is the volume of 100 moles of mercury?", one should refer to the relevant experimental data. It's about molar volume. Such data can be found in the reference literature. So, in one of the tables we find that at 293 K (20 ^oC) the molar volume of the liquid metal in question is 14.81 cm³/mol. In other words, 1 mole of Hg atoms occupies a volume of 14.81 cm^{3. To answer the question of the problem, it is enough to multiply this number by 100.}

Thus, we get the answer: the volume of 100 moles of mercury is equal to 1481 cm3, which practically corresponds to 1.5 liters.

Note that we used the molar volume value for 20 oC. However, the answer received will not change much if mercury is considered under any othertemperature because its coefficient of thermal expansion is very small.

Second solution

Answer the question of how much volume 100 moles of mercury take up using a different approach than the previous one. To do this, we need to use the density and molar mass data for the metal in question.

The initial formula for solving the problem will be the following expression:

ρ=m/V.

Where can I express the value of V:

V=m/ρ.

The mass n=100 mol of a substance is defined as follows:

m=nM.

Where M is the mass of one mole of mercury. Then the working formula for determining the volume will be written as follows:

V=nM/ρ.

The value of the molar mass we have already given above, numerically it is equal to the atomic mass, only expressed in grams per mol (M=200, 59 g/mol). The density of mercury is 13,546 kg/m³ or 13.546 g/cm^{3. We substitute these values into the formula, we get:}

V=nM/ρ=100200, 59/13, 546=1481 cm3.

As you can see, we got exactly the same result as in the previous method of solving the problem.