 ### Note the Pattern

The molar mass of any type of substance is its atomic mass, molecular mass, or formula mass in grams per mole.

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The routine table lists the atomic mass of carbon as 12.011 amu; the average molar mass of carbon—the mass of 6.022 × 1023 carbon atoms—is therefore 12.011 g/mol:

Substance (formula) Atomic, Molecular, or Formula Mass (amu) Molar Mass (g/mol)
carbon (C) 12.011 (atomic mass) 12.011
ethanol (C2H5OH) 46.069 (molecular mass) 46.069
calcium phosphate 310.177 (formula mass) 310.177

The molar mass of naturally developing carbon is different from that of carbon-12 and is not an integer bereason carbon occurs as a mixture of carbon-12, carbon-13, and carbon-14. One mole of carbon still has 6.022 × 1023 carbon atoms, however 98.89% of those atoms are carbon-12, 1.11% are carbon-13, and also a trace (around 1 atom in 1012) are carbon-14. (For more information, view Section 1.6 ) Similarly, the molar mass of uranium is 238.03 g/mol, and also the molar mass of iodine is 126.90 g/mol. When we resolve facets such as iodine and also sulhair, which take place as a diatomic molecule (I2) and also a polyatomic molecule (S8), respectively, molar mass typically refers to the mass of 1 mol of atoms of the element—in this instance I and also S, not to the mass of 1 mol of molecules of the facet (I2 and also S8).

The molar mass of ethanol is the mass of ethanol (C2H5OH) that contains 6.022 × 1023 ethanol molecules. As you calculated in Example 1, the molecular mass of ethanol is 46.069 amu. Due to the fact that 1 mol of ethanol consists of 2 mol of carbon atoms (2 × 12.011 g), 6 mol of hydrogen atoms (6 × 1.0079 g), and also 1 mol of oxygen atoms (1 × 15.9994 g), its molar mass is 46.069 g/mol. Similarly, the formula mass of calcium phosphate is 310.177 amu, so its molar mass is 310.177 g/mol. This is the mass of calcium phosphate that has 6.022 × 1023 formula systems.

The mole is the basis of quantitative nlinux.orgistry. It gives nlinux.orgists through a means to transform conveniently in between the mass of a substance and the variety of individual atoms, molecules, or formula units of that substance. Conversely, it allows nlinux.orgists to calculate the mass of a substance necessary to acquire a wanted number of atoms, molecules, or formula systems. For instance, to transform moles of a substance to mass, we use the relationship

( (moles)(molar ; mass) ightarrowhead mass ag1.71 )

or, more especially,

( molesleft ( dfracgramsmole appropriate ) = grams )​

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### Example 1.7.2

For 35.00 g of ethylene glycol (HOCH2CH2OH), which is supplied in inks for ballpoint pens, calculate the number of

moles. molecules.

Given: mass and also molecular formula

Asked for: number of moles and also variety of molecules

Strategy:

A Use the molecular formula of the compound to calculate its molecular mass in grams per mole.

B Convert from mass to moles by separating the mass provided by the compound’s molar mass.

C Convert from moles to molecules by multiplying the variety of moles by Avogadro’s number.

Solution:

A The molecular mass of ethylene glycol deserve to be calculated from its molecular formula utilizing the approach portrayed in Example 1:

 2C (2 atoms)(12.011 amu/atom) = 24.022 amu 6H (6 atoms)(1.0079 amu/atom) = 6.0474 amu 2O (2 atoms)(15.9994 amu/atom) = 31.9988 amu C2H6O molecular mass of ethanol = 62.068 amu

The molar mass of ethylene glycol is 62.068 g/mol

B The variety of moles of ethylene glycol existing in 35.00 g can be calculated by separating the mass (in grams) by the molar mass (in grams per mole):

( ; 35.00; g; ethylene glycolleft ( frac1; mol; ethylene; glycol; (g))62.068; g; ethylene; glycol ight )=0.5639; mol; ethylene; glycol)

It is constantly an excellent principle to estimate the answer prior to you execute the actual calculation. In this case, the mass given (35.00 g) is less than the molar mass, so the answer must be less than 1 mol. The calculated answer (0.5639 mol) is indeed less than 1 mol, so we have actually probably not made a major error in the calculations.

C To calculate the number of molecules in the sample, we multiply the variety of moles by Avogadro’s number:

( molecules; of; ethylene; glycol=0.5639; molleft ( dfrac6.022 imes 10^231; mol ight ) )

( = 3.396 imes 10^23; molecules​ )

Exercise

For 75.0 g of CCl3F (Freon-11), calculate the number of

moles. molecules.

0.546 mol 3.29 × 1023 molecules

### Example 1.7.3

Calculate the mass of 1.75 mol of each compound.

S2Cl2 (widespread name: sulhair monochloride; systematic name: disulfur dichloride) Ca(ClO)2 (calcium hypochlorite)

Given: number of moles and also molecular or empirical formula

Strategy:

A Calculate the molecular mass of the compound in grams from its molecular formula (if covalent) or empirical formula (if ionic).

B Convert from moles to mass by multiplying the moles of the compound offered by its molar mass.

Solution:

We begin by calculating the molecular mass of S2Cl2 and the formula mass of Ca(ClO)2.

A The molar mass of S2Cl2 is acquired from its molecular mass as follows:

 2S (2 atoms)(32.065 amu/atom) = 64.130 amu 2Cl (2 atoms)(35.353 amu/atom) = 70.906 amu S2Cl​2 molecular mass of S2Cl​2 = 135.036 amu

The molar mass of S2Cl2 is 135.036 g/mol.

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The mass of 1.75 mol of S2Cl2 is calculated as follows:

( moles; S_2Cl_2 left = mass; S_2Cl_2 )

( 1.75; mol; S_2Cl_2left ( dfrac135.036; g; S_2Cl_21;mol;S_2Cl_2 ideal )=236;g; S_2Cl_2 )

B The formula mass of Ca(ClO)2 is obtained as follows:

 1Ca (1 atom )(40.078 amu/atom) = 40.078 amu 2Cl (2 atoms)(35.453 amu/atom) = 70.906 amu 2O (2 atoms)(15.9994 amu/atom) = 31.9988 amu Ca(ClO)2 formula mass of Ca(ClO)2 = 142.983 amu

The molar mass of Ca(ClO)2 is 142.983 g/mol

( moles; Caleft ( ClO ight )_2left < dfracmolar; mass; Caleft ( ClO appropriate )_21; mol; Caleft ( ClO ideal )_2 ideal >=mass; Caleft ( ClO appropriate )_2 )

( 1.75; mol; Caleft ( ClO est )_2left < dfrac142.983; g Caleft ( ClO ideal )_21; mol; Caleft ( ClO est )_2 ideal >=250.; g; Caleft ( ClO ideal )_2 )​

Exercise

Calculate the mass of 0.0122 mol of each compound.

Si3N4 (silsymbol nitride), provided as bearings and also rollers (CH3)3N (trimethylamine), a corrosion inhibitor