The mass formula through density and volume is one of the basic formulas of physics studied within the framework of the school program in the seventh grade. It will come in handy in solving many tasks.

## Mass dependence formula from volume and density

In order to find the density of the liquid or solid, there is a basic formula: the density is equal to the mass divided into volume.

This is written so:

ρ = M / V

And from it you can withdraw two more formulas.

Formula for body volume:

V = m / ρ

As well as a formula for calculating the mass:

**m = v * ρ **

As you can see, remember the latter very easily: this is the only formula where two units need to multiply.

To memorize this dependence, you can use a drawing in the form of a "pyramid", divided into three sections, in the top of which there is a mass, and in the lower corners - density and volume.

**A somewhat different things are dealing with gases. **It is much more difficult to calculate their weight, since gases have no constant density: they dissipate and occupy the entire volume affordable.

For this purpose, the concept of molar mass is useful, which can be found by resolving the mass of all atoms in the formula of substances using data from the periodic table.

The second unit that we need is the amount of substance in the moles. It can be calculated by the reaction equation. You can find more about this within the framework of the Chemistry Course.

Another way to find a molar amount is through the volume of gas to be divided into 22.4 liters. The last number is the volume constant that you should remember.

As a result, knowing the two previous values, we can determine the mass of gas:

**m = n * m, **

where M is a molar mass, and N is the amount of substance.

The result will be in grams, so it is important for solving physical tasks. Do not forget to translate it into a kilogram, dividing 1000. The numbers in this formula can often be found quite complicated, therefore the calculator may be needed.

Another non-standard case with which you can encounter - the need to find **Density of solution **. For this, there is an average density formula, built similarly to the formulas of other average values.

For two substances, it is possible to calculate it like this:

**(M1 + M2) / V1 + V2. **

Also from this formula can be removed several others depending on which of the values are known by the condition of the problem.

## The density table of some substances

The density of many substances is known in advance and easily on the corresponding table.

In working with it, it is important to pay attention to the dimension and do not forget that all data are assembled under normal conditions: room temperature in 20 degrees Celsius, as well as a certain pressure, air humidity, and so on.

The density of others, more rare substances can be found online.

At least one of the density values should be remembered, as it often appears in tasks. it **The density of water is 1000 kg / m3 or 1 g / cm3. **

## Examples of solving problems

### Task 1.

**Condition: **There is an aluminum bar with sides of 3, 5 and 7 centimeters. What is his mass?

**Decision: **

Find the volume of BROs:

V = a * b * c;

V = 3 * 5 * 7 = 105 cm ^{3};

Table value of the density of aluminum: 2800 kg / m ^{3}or 2.8 g / cm ^{3};

We calculate the mass of the bar:

m = v * ρ;

M = 105 * 2,8 = 294

**Answer: **M = 294

### Task 2.

Task on an adjacent topic.

**Condition: **How much energy is required in order to bring water temperature water (20 degrees Celsius) from the glass (200 ml capacity) to boiling point?

**Decision: **

We find the missing information: water boiling point T _{2}= 100 degrees Celsius, specific water heat capacity C = 4200 J / kg * C, water density 1 g / cm ^{3}, 1 ml of water = 1 cm ^{3};

We find a lot of water:

m = v * ρ;

m = 200 * 1 = 200 g = 0.2 kg;

Find energy:

Q = C * M * (T _{2}- T. _{1});

Q = 4200 * 0.2 * (100 - 20) = 67200 J = 67.2 kJ.

**Answer: **Q = 67.2 kJ.

### Task 3.

Task with molar mass.

**Condition: **Find a lot of co. _{2}at a volume of 5.6 liters.

**Decision: **

We find the molar mass of CO _{2 }:

M = 12 + 16 * 2 = 44 g / mol;

Find the amount of substance through the volume:

n = 5.6 / 22.4 = 0.25 mol;

We find a lot:

m = n * m;

m = 0.25 * 44 = 11 g.

**Answer: **m = 11 g