# Explain these three measures of moles: (mass/Mr), (concentration/vol) and (volume/24).

gsenviro | Certified Educator

One can think about a mole as a measure of mass or quantity of a substance. A mole of a substance contains 6.023 x 10^23 atoms (or molecules, if the substance is a compound). That is to say, one mole of the element iron contains 6.023 x 10^23 atoms of iron, while one mole of oxygen gas consists of 6.023 x 10^23 molecules of oxygen gas. One can obtain the moles of a substance by using the three formulas your teacher mentioned:

• The number of moles of a substance is the ratio of the mass of a substance and its molar mass or Mass/Mr. For example, water (H2O) has a molar mass of 18 g, thus, 50 g of water contains 50 g /18 g = 2.78 moles of water.
• The concentration of a solution is often expressed in terms of molarity, which is the ratio of moles of solute to volume of solution. Thus, the number of moles of a solute can be calculated as the product of molarity and volume. For example, 1 lt of 2 molar solution of sulfuric acid contains 1 l x 2 M = 2 moles of acid.
• One mole of a gas occupies 24 lt volume at room temperature, thus the moles of a gas can be calculated as the ratio of volume (in lt) to 24. That is, moles = volume/24.

Thus, the three formula mentioned by your teacher will help you calculate the moles of solids, liquids and gases.

Hope this helps.

aloha968 | Student

A mole is defined as the number equal to the quantity of carbon atoms in exactly 12 grams of pure 12^C.  This number of carbon atoms has been empirically determined to be 6.022 x 10^23.  So a mole, or Avogadro's number, can be thought of as a quantity -- very much like 1 dozen eggs is 12 eggs, 1 mole of eggs is 6.022 x 10^23 eggs.

The mass in grams of one mole of any element (6 x 10^23 atoms) is defined as the molar mass (M) of that element.  An element's molar mass is expressed as the quantity in grams equal to its atomic weight.  So the molar mass (Mr) of sodium (Na) is equal to its atomic weight (amu) in grams which is 22.9 g; 1 mole of Na = 22.9 g = 6 x 10^23 atoms.  For compounds, the masses of the individual atoms are combined to yield the molar mass of the compound.  As an example:

CH4 (methane) has 1 carbon atom (12.1 atomic weight), and 4 hydrogen atoms (1.01 atomic weight).  The molar mass of CH4 (the quantity of 1 mole of methane) is equal to 1 x 12.1 g (carbon component) + 4 x 1.01 g (hydrogen component) = 16.1 g/mole.

If you had 50 g of CH4, then using the equation:

g x 1 mol/Mr = moles

50 g x 1 mole/16.1 g = 3.1 moles

notice grams cancel in this equation

Molarity (M) is a measure of concentration and is defined as the number of moles of solute (dissolved) per liter of solution.  A 1 molar solution of Na (1 M) would have 22.9 g of Na and enough solute to bring the volume to 1 liter.  If 0.435 g KMnO4 (potassium permanganate) is dissolved in enough water to give 250 mL, what is the concentration (M)?

0.435 g KMnO4 x 1 mol KMnO4/158.0 g KMnO4 [Mr] = 0.00275 mol KMnO4

0.00275 mol KMnO4 /0.250 L = 0.0110 M

The ideal gas law is defined as

pressure(P) x volume (V) = n (moles) x R (gas constant) x temperature (T)

The gas constant, R, is determined based on the units.

Rearranging the equation and solving for volume gives ==

V = nRT/P == for n = 1 mole; T = 298.2 °K (room temperature); R = 0.08206 L•atm/mol•K  → V = (1 mol x 0.08206 L•atm/mol• K x 298.2 K)/1 atm = 24.47 L  = volume 1 mole of gas occupies at room temperature

solving the equation for n (moles) gives ==

n = PV/RT, if pressure and temperature are constant, then the number of moles is dependent on the volume, which at room temperature is a multiple of 24.  As an example, 50 L of a gas at room temperature and 1 atmosphere pressure would have 50L/24 = 2.043 moles of gas.

Hope that helps.