Moles and Avogadro's Number: Videos & Practice Problems

In thermodynamics, understanding the relationship between mass, moles, and the number of particles is crucial. A mole, represented by n, corresponds to Avogadro's number, approximately 6.022 × 10²³ particles. The equations n = NN_a and m = nM facilitate conversions between these quantities, enabling calculations of mass, moles, and particle counts effectively.

Moles & Avogadro's Number

In physics and thermodynamics, understanding the relationship between mass, moles, and the number of particles is crucial for calculations involving gases and other materials. The mole, represented by the symbol n, is a unit that quantifies the amount of substance. One mole corresponds to 6.022 × 10²³ particles, a value known as Avogadro's number, denoted as N_A. This concept is similar to a dozen, which signifies 12 items; thus, a mole signifies 6.022 × 10²³ of any given particle, whether atoms, molecules, or even dollars.

To convert between mass, moles, and the number of particles, specific equations are utilized. The number of moles can be calculated from the number of particles using the formula:

n = \frac{N}{N_A}

where N is the number of particles. For example, if you have 8.33 × 10³⁷ carbon atoms, you can find the number of moles by dividing this number by Avogadro's number, resulting in approximately 1.38 × 10¹⁴ moles of carbon.

Conversely, to find the mass from the number of moles, the equation used is:

m = n × M

where M is the molar mass of the substance. For instance, if you have 2.35 moles of aluminum with a molar mass of 26.98 g/mol, the mass can be calculated as:

m = 2.35 × 26.98 = 63.4 g

When starting with mass and needing to find the number of particles, the process involves two steps. First, convert mass to moles using:

n = \frac{m}{M}

For example, if you have 24 g of water (H₂O) with a molar mass of 18.02 g/mol, the number of moles is:

n = \frac{24}{18.02} ≈ 1.33

Next, convert moles to particles using:

N = n × N_A

Thus, N = 1.33 × 6.022 × 10²³ ≈ 8.01 × 10²³ particles of H₂O.

By mastering these conversions and understanding the relationships between mass, moles, and particles, you can effectively navigate thermodynamic calculations and deepen your comprehension of material properties.

If the molar mass of hydrogen is 1.008 g/mol, what is the mass (in grams) of 2 hydrogen atoms?

• A. 0.5004
• B. 3.35 × 10^-24
• C. 2.016
• D. 1.69 × 10^-24

Answer: (B)

Calculating number of water molecules in a bottle

To determine the number of water molecules in a 1.5-liter bottle, we start by recognizing that the molar mass of water (H₂O) is 18 grams per mole. The goal is to find the total number of molecules, denoted as N, using Avogadro's number, which is approximately 6.022 x 10²³ molecules per mole.

First, we need to calculate the number of moles of water, represented as n. The relationship between mass, moles, and molar mass is given by the equation:

n = m / M

where m is the mass in grams and M is the molar mass in grams per mole. Since we know that 1 liter of water has a mass of approximately 1 kilogram, a 1.5-liter bottle of water has a mass of:

m = 1.5 kg = 1500 g

Now, substituting the values into the equation:

n = 1500 g / 18 g/mol = 83.3 moles

Next, we can find the total number of molecules by substituting n into the equation that relates moles to molecules:

N = n × N_A

where N_A is Avogadro's number. Thus, we have:

N = 83.3 moles × 6.022 x 10²³ molecules/mole

Calculating this gives:

N ≈ 5.02 x 10²⁵ molecules

In conclusion, a 1.5-liter bottle of water contains approximately 5.02 x 10²⁵ molecules of H₂O. This calculation illustrates the relationship between volume, mass, moles, and the number of particles in a substance, emphasizing the importance of unit conversions and the use of fundamental constants in chemistry.

Here’s what students ask on this topic:

What is Avogadro's number and why is it important in physics?

Avogadro's number, approximately 6.022 × 10²³, represents the number of particles (atoms, molecules, etc.) in one mole of a substance. It is crucial in physics, especially in thermodynamics, because it allows for the conversion between the macroscopic scale (mass) and the microscopic scale (number of particles). This conversion is essential for understanding and calculating properties of gases, reactions, and other phenomena at the molecular level.

How do you convert between moles and the number of particles?

To convert between moles (n) and the number of particles (N), you use Avogadro's number (N_A). The equation is:

$n=\frac{N}{\mathrm{N_A}}$

For example, if you have 1.2 × 10²⁴ particles, the number of moles is:

$n=\frac{1.2\times {10}^{24}}{6.022\times {10}^{23}}=1.99$

So, you have approximately 1.99 moles.

How do you calculate the mass of a substance from the number of moles?

To calculate the mass (m) of a substance from the number of moles (n), you use the molar mass (M) of the substance. The equation is:

$m=n\times M$

For example, if you have 2.5 moles of aluminum (Al) with a molar mass of 26.98 g/mol, the mass is:

$m=2.5\times 26.98=67.45g$

So, you have 67.45 grams of aluminum.

What is the relationship between mass, moles, and the number of particles?

The relationship between mass (m), moles (n), and the number of particles (N) is interconnected through Avogadro's number (N_A) and the molar mass (M). The key equations are:

$n=\frac{N}{\mathrm{N_A}}$

$m=n\times M$

These equations allow you to convert between the number of particles, the amount of substance in moles, and the mass of the substance. For example, knowing the number of particles and Avogadro's number, you can find the moles, and using the molar mass, you can then find the mass.

How do you find the number of particles in a given mass of a substance?

To find the number of particles (N) in a given mass (m) of a substance, you first convert the mass to moles (n) using the molar mass (M), and then convert moles to particles using Avogadro's number (N_A). The steps are:

1. Calculate moles: $n=\frac{m}{M}$

2. Calculate particles: $N=n\times \mathrm{N_A}$

For example, for 24 grams of H₂O (molar mass = 18.02 g/mol):

$n=\frac{24}{18.02}=1.33$

$N=1.33\times 6.022\times {10}^{23}=8.01\times {10}^{23}$

So, there are approximately 8.01 × 10²³ particles of H₂O.