Atomic Mass Is Equal To

Atomic Mass Is Equal To Protons And
How To Find Atomic Mass
Atomic Mass Is Equal To The Number Of Protons And Neutrons

The atomic mass unit is the system of measurement designed to identify each individual unit of mass in atoms and molecules. Also known as a dalton, the atomic mass unit is a universally-applied measurement based on 1/12 the total mass of a single carbon-12 atom. This means that a carbon-12 atom has the atomic mass of 12 daltons. The designation for a standard atomic mass unit is u or Da. Atomic mass units are used as the system of measurement in every science, except for those involving biology and biochemistry, which use the dalton designation.

One convenient aspect of atomic mass units is that, while based on carbon mass, a single unit is also equal to one hydrogen atom. This is because the combined mass of a single proton and neutron, the composition of a hydrogen atom, is equal to the measurement. Electrons, being only 1/1836 the mass of a proton, are essentially negligible to the overall mass of an atom.

One atomic mass unit is equal to 1/12 of the mass of a single C12 or carbon-12 atom with a value of 1.660 539 066 60 (50) × 10 −27 kg. For example, the mass of a carbon-12 atom equaled to12 amu. As electrons are very light in weight, so, the mass of a carbon-12 isotope is composed of 6 neutrons and 6 protons. Atomic number, chemical symbol, and mass number Carbon has an atomic number of six, and two stable isotopes with mass numbers of twelve and thirteen, respectively. Its average atomic mass is 12.11. Scientists determine the atomic mass by calculating the mean of the mass numbers for its naturally-occurring isotopes. Instant free online tool for Atomic mass unit to gram conversion or vice versa. The Atomic mass unit u to gram g conversion table and conversion steps are also listed. Also, explore tools to convert Atomic mass unit or gram to other weight and mass units or learn more about weight and mass conversions.

One of the most problematic aspects to using the atomic unit of mass to define atoms is that it does not account for the energy that binds together an atom's nucleus. Unfortunately, this is not a fixed mass due to the differences between each different types of atom. As more protons, neutrons and electrons are added to an atom to create a new element, the mass of this binding energy changes. This means that the measurement can be said to be a rough approximation rather than an exact constant.

One of the main uses for the atomic mass unit involves its relationship with moles. A mole is the complete physical quantity of a single unit of a substance. For example, a single water molecule, comprised of two hydrogen atoms and a single oxygen atom, is a mole of water. This means that it has the atomic mass of all three atoms.

The establishment of the atomic mass unit was first started by a chemist name John Dalton in the early 1800s. He used a single hydrogen atom as the platform for the measurement. However, this was altered by Francis Aston with his invention of the mass spectrometer in the late 1800s. Aston defined an atomic mass unit as being 1/16 the mass of a single oxygen-16 atom. It wasn't until 1961 that the International Union of Pure and Applied Chemistry defined the modern applications of the measurement and linked it to carbon-12.

25th Aug 2019 @ 32 min read

In chemistry, the molar mass is an important quantity. It measures the mass of a mole of a given substance.

Definition

The molar mass of a given substance is defined as the mass of a sample divided by the moles of that substance in the sample. In other words, it is the mass per mole of a substance.

It is usually denoted by the symbol M.

Unit

The standard unit is g mol⁻¹. The SI unit is kg mol⁻¹, however, it is very uncommon.

Mole

We know that one mole of a substance consists of 6.022 140 76 × 10²³ elementary particles. This number (aka Avogadro’s constant) is mostly approximated to 6.022 × 10²³. Thus, one mole of carbon contains 6.022 × 10²³ atoms of carbon.

When we say the molar mass of carbon is 12.0 g mol⁻¹, it means one mole of carbon weighs 12.01 g. In other words, 6.022 × 10²³ atoms of carbon weigh 12.01 g.

Important of Molar Mass

In chemistry, calculations are related to chemical reactions and stoichiometry. Calculations often include quantities like molarity, molality, mole fraction, molar volume. All these involve the number of moles. Although there is no direct way to measure the number of moles of any substance, the number of moles can be calculated by knowing the molar mass of the substance. The molar mass links the mass of a substance to its moles. Thus, by knowing the molar mass, we can determine the number of moles contained in a given mass of a sample.

Let me make it more clear with an example of sodium chloride. The molar mass of sodium chloride is known; it is 58.44 g mol⁻¹. If we have to measure one mole of sodium chloride, there is no instrument that can directly measures it. But we know 58.44 g of sodium chloride is equivalent to one mole of it. So, we measure 58.44 g of NaCl with a weight scale, which is equivalent to one of 58.44 g. Hence, we have one mole of NaCl measured.

Some of the important points regarding the molar mass are as follows:

It is a bulk property, not atomic property, of a substance.
It is an intensive property. So, it does not vary with the size of a sample.
It is dependents on percentages of consistents of a sample. Thus, it can vary with a terrestrial location.
It is used to convert the mass of a substance to its mole and vice versa.

Atomic Mass and Molar Mass

The atomic mass and the molar mass are confused with one another. But they are two different quantities with a definition. The table below describes the differences between the two.

Table 1: Difference between Atomic Mass and Molar Mass
Atomic Mass	Molar Mass
The atomic mass is the sum of the mass of protons, neutrons, and electrons.	It is the mass of a mole of a substance.
It is denoted by m_a.	The symbol used for it is M.
It has a unit of the unified mass unit (u) or the atomic mass unit (amu).	g mol⁻¹ is the standard unit for the molar mass.
The atomic mass is an atomic property.	It is a bulk property.
It does not account for isotopes.	The existence of isotopes is accounted for since it is a bulk property.
The atomic mass is constant for a particular isotopic element. It does not vary from sample to sample. For example, the atomic mass of carbon-12 is 12 u. This is true for all atoms of carbon-12 in the universe.	It could vary from sample to sample depending on the percentages of constituents in the sample.

Average Atomic Mass to Molar mass

If the average atomic mass (m_a) or average molecular mass is known, we can convert it into the molar mass (M) with the help of the molar mass constant (M_u).

The average atomic mass is measured in the unified mass unit (u). The unified mass unit is related to the molar mass constant (M_u) by the Avogadro constant (N_A).

m_a is the average atomic mass or the average mass of an atom. So, the mass of a mole of the atom is m_a × N_A. But this quantity is in the unified mass unit (u). The above equation can convert u to g mol⁻¹.

Therefore, the average atomic mass divided by one unified mass unit times the molar mass constant results in the molar mass.

The precise value of M_u is 0.999 999 999 65(30) g mol⁻¹. But this value approximately equals 1 g mol⁻¹.

From the above equation, we can say the numeric value of the molar mass and the average atomic mass is approximately equal. This is also true for molecules. The table below lists the elements (and the compounds) with the average atomic mass and the average molar mass.

Table 2: Average Atomic Mass to Molar Mass
Element (or Compund)	Average Atomic Mass (or Average Molecular Mass) (u)	Divide (÷)	Unified Mass Unit (u)	Multiple (×)	Molar Mass Constant (M_u)	Equal to (=)	Molar Mass (1 g mol⁻¹)
Hydrogen (H)	1.008 u	÷	1 u	×	1 g mol⁻¹	=	1.008 g mol⁻¹
Carbon (C)	12.011 u	÷	1 u	×	1 g mol⁻¹	=	12.011 g mol⁻¹
Oxygen (O)	15.999 u	÷	1 u	×	1 g mol⁻¹	=	15.999 g mol⁻¹
Nitrogen (N)	14.007 u	÷	1 u	×	1 g mol⁻¹	=	14.007 g mol⁻¹
Potassium (K)	39.098 u	÷	1 u	×	1 g mol⁻¹	=	39.098 g mol⁻¹
Calcium (Ca)	40.078 u	÷	1 u	×	1 g mol⁻¹	=	40.078 g mol⁻¹
Chlorine (Cl)	35.45 u	÷	1 u	×	1 g mol⁻¹	=	35.45 g mol⁻¹
Hydrogen Gas (H₂)	2.016 u	÷	1 u	×	1 g mol⁻¹	=	2.016 g mol⁻¹
Water (H₂O)	18.015 u	÷	1 u	×	1 g mol⁻¹	=	18.015 g mol⁻¹
Methane (CH₄)	16.04 u	÷	1 u	×	1 g mol⁻¹	=	16.04 g mol⁻¹
Nitrogen Dioxide (NO₂)	46.006 u	÷	1 u	×	1 g mol⁻¹	=	46.006 g mol⁻¹
Ammonia (NH₃)	17.031 u	÷	1 u	×	1 g mol⁻¹	=	17.031 g mol⁻¹
Glucose (C₆H₁₂O₆)	180.156 u	÷	1 u	×	1 g mol⁻¹	=	180.156 g mol⁻¹

Atomic Weight to Molar Mass

The atomic weight (aka relative atomic mass) (A_r) is a dimensionless quantity having the numeric value of the average atomic mass. The average atomic mass and atomic weight are related by the following equation.

From the above two equations,

Therefore, the atomic weight times the molar mass constant results in the molar mass.

So, we can calculate the molar mass of any compound in the same way we calculate the atomic weight from its constituent elements.

Consider an example of glucose. Glucose molecular formula is C₆H₁₂O₆; it has six carbons, twelve hydrogens, and six oxygens. The molar mass of glucose is the sum of the relative atomic mass of all the atoms in the molecular formula.

Table 3: Molar Mass of Glucose (C₆H₁₂O₆)
Element	Atomic Weight	Molar Mass (g mol⁻¹)
Carbon (C)	12.011	12.011
Hydrogen (H)	1.008	1.008
Oxygen (O)	15.999	15.999
Molar Mass of Glucose (C₆H₁₂O₆)		180.156

Molar Mass of Mixtures

The molar mass of a mixture is determined using the mole fraction (x_i).

where: M_mix is the molar mass of a mixture of n components, and x_i and M_i are the mole fraction and the molar mass of i^th component.

The above formula can also be expressed in terms of the mass fraction w_i.

Consider a liquid-liquid mixture of water (H₂O) and ethanol (C₂H₆O). Water is 20 % and ethanol, 80 %.

The molar mass of pure water is M_H₂O.

Similarly, for ethanol,

The molar mass of the mixture is M_mix.

Thus,

Measurement of Molar Mass

From Atomic Weight

The measurement from the atomic weight is the most reliable and precise method in comparison to others. The atomic weight is determined from the atomic mass and distribution of isotopes. The precision in the molar mass depends upon the precision in the measurement of the atomic weight, which depends on the atomic mass and the percentages of isotopes. Today, with the help of mass spectrometry, we are able to achieve high precision in the atomic mass.

The value of molar mass calculated from the atomic weight are reliable for all practical calculations.

From Vapour Density

The vapour density (ρ) is the mass of vapour to its volume. We are familiar with the ideal gas equation.

Here, P is the pressure of a gas occupying the volume V at the temperature T. n and R are the moles of the gas and the ideal gas constant.

Now, the number of moles (n) is the mass of the gas divided by the molar mass (M).

Using the above two equations,

If we are able to determine the vapour density of a sample of gas for a known pressure and temperature, we can estimate the molar mass of the vapour from the above equation.

From Freezing-Point Depression

When a non-volatile solute is added into a solvent, the freezing point of the solvent decreases. This decrease is called freezing-point depression. Freezing-point depression ∆T_F = T_Fsolvent − T_Fsolution depends on the concentration (molality) of the solute and is governed by the equation below.

Here, ∆T is freezing-point depression, K_F is the solvent dependent cryoscopic constant, b is the molality, and i is the van ‘Hoff factor (number of ions formed after the dissociation of the solute).

For a very dilute solution, .

By knowing ∆T_F, K_F, w_solute, and i, we can determine the molar mass, M_solute.

From Boiling-Point Elevation

Boiling-point elevation is the rise in the boiling point of a solvent due to the presence of a non-volatile solute. Similar to freezing-point depression, the rise in the boiling point depends upon the molality.

Here, ∆T_B = T_solution − T_solute is boiling-point elevation, K_B is the ebullioscopic constant, b is the molality, and i is the van ‘t Hoff factor.

For a very dilute solution,

By knowing ∆T_B, K_B, w_solute, and i, we can determine the molar mass, M_solute.

Examples and Calculations

Example 1: To Determine Molar Mass of Oleic Acid

Oleic acid is a odourless fatty acid having a molecular formula of C₁₈H₃₄O₂. It has eighteen carbons, thirty-four hydrogens, and two oxygens.

Table 4: Molar Mass of Oleic Acid, C₁₈H₃₄O₂
Element	Number of Atom	Molar Mass (g mol⁻¹)	Total
Carbon (C)	18	12.011	216.198
Hydrogen (H)	34	1.008	34.272
Oxygen (O)	2	15.999	31.998
Molar Mass of Oleic Acid, (C₁₈H₃₄O₂)			282.468 g mol ⁻¹

Therefore, the molar of oleic acid is 282.468 g mol⁻¹.

Example 2: To Determine Molar Mass of Reinecke’s Salt

Reinecke’s salt is a red crystalline salt with chromium in the centre as shown in the above figure. The chromium atom is surrounded by six nitrogens, four carbons, and four sulphur. The molecular formula is C₄H₁₂N₇OCrS₄.

Table 5: Molar Mass of Reinecke's Salt, C₄H₁₂N₇OCrS₄
Element	Number of Atom	Molar Mass (g mol⁻¹)	Total
Carbon (C)	4	12.011	48.044
Hydrogen (H)	12	1.008	12.096
Nitrogen (N)	7	14.007	98.049
Oxygen (O)	1	15.999	15.999
Chromium (Cr)	1	51.996	51.996
Sulphur (S)	4	32.065	128.26
Molar Mass of Reinecke’s Salt, C₄H₁₂N₇OCrS₄			354.444 g mol⁻¹

Example 3: To Determine Molar Mass of Air

Air is a mixture. It mainly consists 79 % nitrogen (N₂) and (21 %) oxygen (O₂). Other components are argon (Ar), carbon dioxide, (CO₂), water (H₂O), helium (He) etc., but these components are in small fraction and can be ignored.

The molar mass of nitrogen (N₂) and oxygen (O₂) are 28.014 g mol⁻¹ and 31.998 g mol⁻¹ respectively.

Table 6: Molar Mass of Air
Molecules	Fraction	Molar Mass (g mol⁻¹)	Total
Nitrogen (N₂)	0.79	28.014	22.13
Oxygen (O₂)	0.21	31.998	5.88
Molar Mass of Air			≈ 28 g mol⁻¹

Therefore, the molar of air is 28 g mol⁻¹.

Example 4: To Determine Molar Mass of Sodium Chloride Solution

Sodium chloride a common salt. It is white and odourless powder. Consider a solution of 50 % NaCl. 100 g of the solution consists of 50 g of NaCl and 50 g of H₂O.

The molar mass of water is 2 × 1.008 + 15.999 = 18.015 g mol⁻¹ and of sodium chloride is 22.99 + 35.45 = 58.44 g mol⁻¹.

The molar of the solution is calculated as follows:

Thus, the molar mass of 50 % sodium chloride solution is 28 g mol⁻¹.

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