Mole Concept And Molar Masses

Step 1: Formula for number of moles.
The number of moles is given by:
Step 2: Substituting values.
The molar mass of water is: The given mass of water is .
Step 3: Correct option.
Thus, the number of moles in 180 g of water is 10.
Final Answer:

Step 1: Formula for number of moles.

Step 2: Molar mass of water.
Molar mass of H O = g mol .

Step 3: Substitution.

Step 4: Conclusion.
Thus, 180 g of water contains 10 moles.

Final Answer:

Moles of water can be calculated using:

Step 1: Understanding the Unit of First-Order Reaction For a first-order reaction, the rate equation is: where is the rate constant. Since rate has units of and concentration has units of , the unit of is:

Step 1: The formula for molar conductivity ( ) is: where S cm and M. Step 2: Substituting values:

Step 1: Introduction to CFT Crystal Field Theory (CFT) explains the splitting of d-orbitals in transition metal complexes due to ligand interaction. Step 2: Octahedral Splitting In an octahedral field, d-orbitals split into two energy levels: - (lower energy): - (higher energy): Step 3: High-Spin vs Low-Spin Complexes - Weak-field ligands (Cl , H O) → High-spin, small
- Strong-field ligands (CN , CO) → Low-spin, large

Step 1: Definition of Osmotic Pressure Osmotic pressure ( ) is the pressure required to stop the flow of solvent molecules through a semipermeable membrane. Step 2: Van't Hoff Equation for Osmotic Pressure where:
- = Concentration of solute (mol L )
- = Universal gas constant
- = Temperature (Kelvin) Step 3: Finding Molar Mass of Solute Since concentration ( ) is given by and , we substitute: Rearranging for molar mass :

Step 1: Definition of Mole Fraction Mole fraction ( ) of a component in a mixture is the ratio of the number of moles of that component to the total number of moles in the mixture. Step 2: Example Consider a solution containing 2 moles of ethanol ( ) and 3 moles of water ( ).

Step 1: Definitions - Order of a reaction: The sum of the powers of concentration terms in the rate law.
- Molecularity: The number of reacting species involved in an elementary reaction. Step 2: Example For the reaction: If the rate law is: - The order of reaction is .
- If the reaction occurs in one step with three reactants colliding, its molecularity is 3.

Step 1: The van't Hoff factor ( ) is determined using: Since the solutions are isotonic, their osmotic pressures are equal: Step 2: Given: Step 3: Solve for : Thus, the van't Hoff factor for NaCl is 1.95.

Assume of solution urea and water.
Moles of urea .
Moles of water .
Total moles .
Mole fraction of urea .
Mole fraction of water .

Step 1: Recall the formula.

Step 2: Write known values.
- Molarity = 0.2 M
- Molar mass of H SO = (2 × 1) + (32) + (16 × 4)
= 2 + 32 + 64
= 98 g/mol

Step 3: Calculate concentration.
But since we want concentration per litre (1000 ml): Step 4: Final Answer.
Thus, the concentration of 0.2 M H SO solution is:

Let us consider 100 g of solution.
Mass of water = 54 g, Mass of ethanol = 46 g.

Step 1: Calculate moles of water.
Molar mass of water = 18 g mol .
Moles of water = mol.

Step 2: Calculate moles of ethanol.
Molar mass of ethanol = 46 g mol .
Moles of ethanol = mol.

Step 3: Total moles.
Total moles = mol.

Step 4: Mole fractions.
Mole fraction of water = .
Mole fraction of ethanol = .

Step 1: Recall the formula.
The mass of solute required is calculated by:

Step 2: Write known values.
- Molarity (M) = 0.2 M
- Volume (V) = 500 ml = 0.5 L
- Molar mass of Na CO = (23 2) + 12 + (16 3) = 46 + 12 + 48 = 106 g/mol

Step 3: Calculate mass.
Step 4: Final Answer.
Thus, to prepare 500 ml of 0.2 M Na CO solution, 10.6 g of Na CO is required.

Molarity (M):
Molarity is defined as the number of moles of solute present in 1 litre of solution.

Example:
If 58.5 g of NaCl (molar mass = 58.5 g/mol) is dissolved in water to make 1 litre of solution, then:

--- Molality (m):
Molality is defined as the number of moles of solute present in 1 kg of solvent.

Example:
5.0 g of ethanoic acid ( , molar mass = 60 g/mol) is dissolved in 150 g (0.150 kg) of benzene:


So, the molality is .

Step 1: Calculate number of moles of KOH.

Step 2: Convert volume of solution into litres.

Step 3: Apply molarity formula.

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. The formula for molality is: Where: - is the number of moles of solute (in this case, ethanoic acid),
- is the mass of the solvent (benzene) in kilograms.
We are given:
- Mass of ethanoic acid ,
- Mass of benzene ,
- Molar mass of ethanoic acid .
Step 1: Calculate the number of moles of ethanoic acid (solute).
The number of moles is calculated by the formula: Step 2: Calculate molality using the formula.
Now, we can use the formula for molality: Thus, the molality of the solution is .

We are given 30 mass percent benzene in the solution. This means:
- Mass of benzene = 30 g
- Mass of carbon tetrachloride (CCl ) = 70 g
Molar masses:
- Molar mass of benzene (C H ) = 78 g/mol
- Molar mass of carbon tetrachloride (CCl ) = 154 g/mol

Step 1: Calculate moles of benzene.

Step 2: Calculate moles of carbon tetrachloride.

Step 3: Calculate mole fraction of benzene.
Thus, the mole fraction of benzene is 0.458.

Step 1: Recall definition of ppm.
For dilute aqueous solutions, 1 ppm corresponds to 1 part of solute per parts of solution (by mass). Practically, in water:

Step 2: Apply this to the given value.
Given concentration = 3.5 ppm. Therefore, in terms of mg/L:

Step 3: Match with options.
Option (C) matches: .