To determine the number of grams of H2O present in 0.75 moles of H2O, we first need to understand what a mole represents. A mole is a standard unit used to measure the quantity of a substance. It relates the mass of a substance to the amount of particles (atoms, molecules, ions, etc.) present in the substance.

One mole represents 6.022 x 10^23 particles of a substance. This number is known as Avogadro’s number. So for any substance, one mole contains 6.022 x 10^23 representative particles. The mass of one mole of a substance in grams is equal to its molar mass. Molar mass is the mass of one mole of a substance expressed in grams per mole. It is calculated by summing the atomic masses of the constituent atoms in the molecule.

## Calculating the Molar Mass of H2O

To find the molar mass of H2O, we first need to know its molecular formula. The molecular formula of water is H2O, indicating it contains two hydrogen atoms and one oxygen atom.

The molar mass can be calculated as:

Molar mass of H (hydrogen) = 1.0079 g/mol

Molar mass of O (oxygen) = 15.9994 g/mol

So, molar mass of H2O = (2 x molar mass of H) + (molar mass of O)

= (2 x 1.0079 g/mol) + 15.9994 g/mol

= 18.0153 g/mol

Therefore, the molar mass of water H2O is 18.0153 grams per mole.

## Finding the Number of Grams in 0.75 Moles of H2O

Now that we know the molar mass of H2O, we can use it to find the number of grams present in 0.75 moles of H2O.

Using the relationship:

Number of moles x molar mass = grams

We get:

0.75 moles of H2O x 18.0153 g/mol = 13.5115 g

Therefore, the number of grams of H2O present in 0.75 moles of it is 13.5115 g.

## Showing the Calculation Step-by-Step

Let’s go through the calculation step-by-step:

- Calculate the molar mass of H2O:

Molar mass of H = 1.0079 g/mol

Molar mass of O = 15.9994 g/mol

Molar mass of H2O = (2 x 1.0079 g/mol) + 15.9994 g/mol = 18.0153 g/mol - Number of moles of H2O given = 0.75 moles
- Use the formula:

Number of moles x molar mass = grams

0.75 moles x 18.0153 g/mol = 13.5115 g

Therefore, 0.75 moles of H2O contains 13.5115 grams of H2O.

## Explaining the Concept Behind the Calculation

The calculation relies on two important concepts in chemistry:

**Mole:**The mole is used to represent a specific number of particles – 6.022 x 10^23. So 1 mole of any substance contains 6.022 x 10^23 particles of that substance. Moles provide a link between the mass of a substance and the number of particles it contains.**Molar mass:**The molar mass of a substance expressed in g/mol gives the mass of 1 mole of that substance. It bridges the mass of a substance to the number of moles.

Using these two concepts:

- We calculated the molar mass of H2O as 18.0153 g/mol. This tells us the mass of 1 mole of H2O.
- We were given the number of moles of H2O as 0.75 moles.
- Using the formula: moles x molar mass = grams, we found the grams of H2O corresponding to 0.75 moles.
- 0.75 moles x 18.0153 g/mol gave 13.5115 grams.

Therefore, the calculation uses the concepts of mole and molar mass to convert between mass and amount of a substance.

## Why the Result Makes Sense

The result we got – 13.5115 grams for 0.75 moles of H2O – makes sense based on the principles used:

- 0.75 moles is less than 1 mole.
- The molar mass of H2O (18.0153 g/mol) gives the mass for 1 mole.
- Since we have less than 1 mole (0.75 moles), the mass should be less than the molar mass.
- 0.75 x 18.0153 g/mol rightly gives 13.5115 g, which is less than 18.0153 g.

Therefore, the result is logical and consistent with the principles of mole and molar mass used in the calculation.

## Applications of the Concept

The mole concept is very useful in various chemical calculations involving mass-amount relationships. Some examples of application include:

**Determining percentage composition:**Moles are used to calculate the percentage mass contribution of each element in a compound.**Balancing chemical equations:**Chemical equations have to be balanced in terms of moles of reactants and products.**Finding formula units:**The formula unit of an ionic compound is found using the smallest whole number ratio of moles of cations to anions.**Determining limiting reagent:**For a chemical reaction, the moles of reactants are compared to identify the limiting reagent which will get used up first.

The mole is thus a fundamental concept with wide applications in stoichiometry, solution chemistry, analytical chemistry, etc.

## Examples and Practice Problems

Let’s go through some examples and practice problems using the mole concept:

### Example 1

Calculate the number of moles present in 34 grams of CuSO4

**Solution:**

- Molar mass of CuSO4 = 159.6 g/mol
- Use formula: moles = mass/molar mass
- Moles of CuSO4 = 34 g / 159.6 g/mol = 0.213 moles

### Example 2

12.044 x 10^23 molecules of methane (CH4) are present. How many moles is this?

**Solution:**

- 1 mole CH4 = 6.022 x 10^23 molecules (Avogadro’s number)
- Given molecules = 12.044 x 10^23
- Moles = Given molecules / Avogadro’s number
- Moles of CH4 = 12.044 x 10^23 molecules / 6.022 x 10^23 molecules/mol = 2 moles

### Practice Problem 1

Find the mass of 0.5 moles of ethanoic acid (CH3COOH)

**Solution:**

- Molar mass CH3COOH = 60 g/mol
- Moles given = 0.5 moles
- Use formula: Mass = Moles x Molar mass
- Mass = 0.5 moles x 60 g/mol = 30 grams

### Practice Problem 2

How many molecules are present in 0.1 mole of glucose (C6H12O6)?

**Solution:**

- molecules in 1 mole = 6.022 x 10^23 (Avogadro’s number)
- Moles of glucose given = 0.1 moles
- Number of molecules = Moles x Avogadro’s number
- Number of molecules = 0.1 moles x (6.022 x 10^23 molecules/mol) = 6.022 x 10^22

These examples illustrate the usefulness of the mole concept in various stoichiometry calculations. With practice, the conversion between mass, moles and number of particles can be easily mastered.

## Mole Concept in the Real World

The mole is very important in chemistry and stoichiometry. Here are some real-world examples of its application:

**Medicines and drugs:**The molar amounts are carefully calculated during preparation of medicines and drugs.**Chemical industry:**In chemical plants and refineries, stoichiometric amounts are used based on mole ratios to optimize yield and minimize costs.**Environmental monitoring:**The concentration of pollutants like ozone, SO2, NOx are given in moles/volume units for regulatory standards.**Atomic weight standards:**The mole is used to determine and standardize atomic weights of elements with high precision.**Food and nutrition research:**The mole concept is applied to determine molar quantities of nutrients, vitamins and minerals in foods.

Therefore, the principles of the mole and molar mass are indispensable for chemists and chemical engineers working in various industries, laboratories and regulatory agencies.

## Conclusion

To summarize, the number of grams of H2O present in 0.75 moles of it is 13.5115 grams.

This was calculated using:

- Molar mass of H2O = 18.0153 g/mol
- Moles of H2O given = 0.75 moles
- Formula used: Grams = Moles x Molar mass

The mole is an essential concept in stoichiometry and applied chemistry, allowing conversion between mass and amount of substance. With an understanding of molar mass and mole concept, various stoichiometric calculations can be easily performed.