What are the different formulas that define a mole?

Jan 8, 2014

There is only one definition of a mole. A mole is the quantity of a substance that has the same number of particles as are found in exactly 12 g of carbon-12. This number, Avogadro's number, is 6.022 × 10²³.

This definition, however, leads to several different methods for determining the number of moles of a substance based on the
Number of particles
Molar mass
Volume and molarity of a solution
Ideal Gas Law

FROM NUMBER OF PARTICLES

n = number of molecules)/Avogadro’s Number

Example:
How many moles of oxygen are contained in 2.25 x 10²⁴ molecules?

n = number of molecules/Avogadro’s Number =
2.25 × 10²⁴ molecules × (1 mol)/(6.022 × 10²³ molecules) = 3.74 mol

FROM MOLAR MASS

n = $\frac{m a s s}{m o l a r m a s s}$

Example:
How many moles are in 98.0 g MnO₂?

n = $\frac{m a s s}{m o l a r m a s s}$ = 98.0 g MnO₂ × (1 mol MnO₂)/(86.94 g MnO₂) = 1.13 mol MnO₂

FROM VOLUME AND MOLARITY OF A SOLUTION

n = volume × molarity or

n = litres × moles/litres

Example:
How many moles of aluminum nitrate, Al(NO₃)₃, are in 3.00 L of a 0.340 mol/L solution of aluminum nitrate?

n = 3.00 L Al(NO₃)₃ × (0.340 mol Al(NO₃)₃)/(1 L Al(NO₃)₃) = 1.02 mol Al(NO₃)₃

FROM THE IDEAL GAS LAW

n = $\frac{P V}{R T}$

Example:
Calculate the number of moles of hydrogen gas in an 80.5 mL sample collected at 25 °C and 0.976 atm.

n = (PV)/(RT) = (0.976 atm × 0.0805 L)/(0.08206 L•atm•K⁻¹mol⁻¹ × 298 K) =
3.21 × 10⁻³ mol

There are, of course, other methods for determining the number of moles, but these are the most common methods that are used in the early stages of chemistry.

Jan 8, 2014

There is only one definition of a mole. A mole is the quantity of a substance that has the same number of particles as are found in exactly 12 g of carbon-12. This number, Avogadro's number, is 6.022 × 10²³.

This definition, however, leads to several different methods for determining the number of moles of a substance based on the
Number of particles
Molar mass
Volume and molarity of a solution
Ideal Gas Law

FROM NUMBER OF PARTICLES

n = number of molecules/Avogadro’s Number

Example:
How many moles of oxygen are contained in 2.25 x 10²⁴ molecules?

n = number of molecules/Avogadro’s Number =
2.25 × 10²⁴ molecules × (1 mol)/(6.022 × 10²³ molecules) = 3.74 mol

FROM MOLAR MASS

n = $\frac{m a s s}{m o l a r m a s s}$

Example:
How many moles are in 98.0 g MnO₂?

n = $\frac{m a s s}{m o l a r m a s s}$ = 98.0 g MnO₂ × (1 mol MnO₂)/(86.94 g MnO₂) = 1.13 mol MnO₂

FROM VOLUME AND MOLARITY OF A SOLUTION

n = volume × molarity or

n = litres × moles/litres

Example:
How many moles of aluminum nitrate, Al(NO₃)₃, are in 3.00 L of a 0.340 mol/L solution of aluminum nitrate?

n = 3.00 L Al(NO₃)₃ × (0.340 mol Al(NO₃)₃)/(1 L Al(NO₃)₃) = 1.02 mol Al(NO₃)₃

FROM THE IDEAL GAS LAW

n = $\frac{P V}{R T}$

Example:
Calculate the number of moles of hydrogen gas in an 80.5 mL sample collected at 25 °C and 0.976 atm.

n = (PV)/(RT) = (0.976 atm × 0.0805 L)/(0.08206 L•atm•K⁻¹mol⁻¹ × 298 K) =
3.21 × 10⁻³ mol

There are, of course, other methods for determining the number of moles, but these are the most common methods that are used in the early stages of chemistry.

Jan 8, 2014

There is only one definition of a mole. A mole is the quantity of a substance that has the same number of particles as are found in exactly 12 g of carbon-12. This number, Avogadro's number, is 6.022 × 10²³.

This definition, however, leads to several different methods for determining the number of moles of a substance based on the
Number of particles
Molar mass
Volume and molarity of a solution
Ideal Gas Law

FROM NUMBER OF PARTICLES

n = number of molecules/Avogadro’s Number

Example:
How many moles of oxygen are contained in 2.25 x 10²⁴ molecules?

n = number of molecules/Avogadro’s Number =
2.25 × 10²⁴ molecules × (1 mol)/(6.022 × 10²³ molecules) = 3.74 mol

FROM MOLAR MASS

n = mass/molar mass

Example:
How many moles are in 98.0 g MnO₂?

n = $\frac{m a s s}{m o l a r m a s s}$ = 98.0 g MnO₂ × (1 mol MnO₂)/(86.94 g MnO₂) = 1.13 mol MnO₂

FROM VOLUME AND MOLARITY OF A SOLUTION

n = volume × molarity or

n = litres × moles/litres

Example:
How many moles of aluminum nitrate, Al(NO₃)₃, are in 3.00 L of a 0.340 mol/L solution of aluminum nitrate?

n = 3.00 L Al(NO₃)₃ × (0.340 mol Al(NO₃)₃)/(1 L Al(NO₃)₃) = 1.02 mol Al(NO₃)₃

FROM THE IDEAL GAS LAW

n = $\frac{P V}{R T}$

Example:
Calculate the number of moles of hydrogen gas in an 80.5 mL sample collected at 25 °C and 0.976 atm.

n = (PV)/(RT) = (0.976 atm × 0.0805 L)/(0.08206 L•atm•K⁻¹mol⁻¹ × 298 K) =
3.21 × 10⁻³ mol

There are, of course, other methods for determining the number of moles, but these are the most common methods that are used in the early stages of chemistry.

Jan 8, 2014

There is only one definition of a mole. A mole is the quantity of a substance that has the same number of particles as are found in exactly 12 g of carbon-12. This number, Avogadro's number, is 6.022 × 10²³.

This definition, however, leads to several different methods for determining the number of moles of a substance based on the
Number of particles
Molar mass
Volume and molarity of a solution
Ideal Gas Law

FROM NUMBER OF PARTICLES

n = number of particles/Avogadro’s Number

Example:
How many moles of oxygen are contained in 2.25 x 10²⁴ molecules?

n = number of molecules/Avogadro’s Number =
2.25 × 10²⁴ molecules × (1 mol/6.022 × 10²³ molecules) = 3.74 mol

FROM MOLAR MASS

n = $\frac{m a s s}{m o l a r m a s s}$

Example:
How many moles are in 98.0 g MnO₂?

n = $\frac{m a s s}{m o l a r m a s s}$ = 98.0 g MnO₂ × (1 mol MnO₂)/(86.94 g MnO₂) = 1.13 mol MnO₂

FROM VOLUME AND MOLARITY OF A SOLUTION

n = volume × molarity or

n = litres × moles/litres

Example:
How many moles of aluminum nitrate, Al(NO₃)₃, are in 3.00 L of a 0.340 mol/L solution of aluminum nitrate?

n = 3.00 L Al(NO₃)₃ × (0.340 mol Al(NO₃)₃)/(1 L Al(NO₃)₃) = 1.02 mol Al(NO₃)₃

FROM THE IDEAL GAS LAW

n = $\frac{P V}{R T}$

Example:
Calculate the number of moles of hydrogen gas in an 80.5 mL sample collected at 25 °C and 0.976 atm.

n = (PV)/(RT) = (0.976 atm × 0.0805 L)/(0.082 06 L•atm•K⁻¹mol⁻¹ × 298 K) =
3.21 × 10⁻³ mol

There are, of course, other methods for determining the number of moles, but these are the most common methods that are used in the early stages of chemistry.