A solution is prepared by dissolving 38 g of H2S04 in 220 g water. If the density of the solution is 1.96 g/ml, find its:
molality
molarity
mole fraction of the components of the solution
normality
This assignment is needed tomorrow. I really don't know the answer. I tried asking for help on other websites these weekend but no one answered. Please show your solutions on how did you find the answers. Thanks.
To find the molality of the solution, we need to calculate the moles of solute (H2SO4) and then divide it by the mass of the solvent (water) in kilograms.
Step 1: Calculate the moles of H2SO4:
The molar mass of H2SO4 is 98 g/mol.
moles of H2SO4 = mass / molar mass
moles of H2SO4 = 38 g / 98 g/mol
moles of H2SO4 ≈ 0.3878 mol
Step 2: Calculate the mass of water in kilograms:
mass of water = 220 g
mass of water = 220 g / 1000 (to convert grams to kilograms)
mass of water = 0.22 kg
Step 3: Calculate the molality:
molality = moles of solute / mass of solvent in kilograms
molality = 0.3878 mol / 0.22 kg
molality ≈ 1.76 mol/kg
Therefore, the molality of the solution is approximately 1.76 mol/kg.
To find the molarity of the solution, we need to calculate the moles of solute (H2SO4) and then divide it by the volume of the solution in liters.
Step 1: Calculate the molality of H2SO4:
We already found the moles of H2SO4 previously: 0.3878 mol.
Step 2: Calculate the volume of the solution in liters:
The density of the solution is given as 1.96 g/ml.
volume of the solution = mass / density
volume of the solution = (38 g + 220 g) / 1.96 g/ml
volume of the solution = 258 g / 1.96 g/ml
volume of the solution ≈ 131.63 ml
Converting ml to liters:
volume of the solution = 131.63 ml x (1 L / 1000 ml)
volume of the solution ≈ 0.13163 L
Step 3: Calculate the molarity:
molarity = moles of solute / volume of solution in liters
molarity = 0.3878 mol / 0.13163 L
molarity ≈ 2.947 M
Therefore, the molarity of the solution is approximately 2.947 M.
To find the mole fraction of the components of the solution, we need to calculate the moles of solute (H2SO4) and the moles of solvent (water), and then divide them by the total moles.
Step 1: Calculate the moles of H2SO4 (solute):
We already found the moles of H2SO4 previously: 0.3878 mol.
Step 2: Calculate the moles of water (solvent):
The molar mass of water (H2O) is 18 g/mol.
moles of water = mass / molar mass
moles of water = 220 g / 18 g/mol
moles of water ≈ 12.222 mol
Step 3: Calculate the mole fraction of each component:
mole fraction of H2SO4 = moles of H2SO4 / total moles
mole fraction of H2SO4 = 0.3878 mol / (0.3878 mol + 12.222 mol)
mole fraction of H2SO4 ≈ 0.0309
mole fraction of water = moles of water / total moles
mole fraction of water = 12.222 mol / (0.3878 mol + 12.222 mol)
mole fraction of water ≈ 0.9691
Therefore, the mole fraction of H2SO4 in the solution is approximately 0.0309, and the mole fraction of water in the solution is approximately 0.9691.
To find the normality of the solution, we need to consider the acidic nature of H2SO4, which can give off two moles of H+ ions per mole of H2SO4.
Step 1: Calculate the equivalent moles of H2SO4:
equivalent moles of H2SO4 = moles of H2SO4 × number of H+ ions
equivalent moles of H2SO4 = 0.3878 mol × 2
equivalent moles of H2SO4 ≈ 0.7756 eq
Step 2: Calculate the volume of the solution in liters:
We already found the volume of the solution previously: 0.13163 L.
Step 3: Calculate the normality:
normality = equivalent moles of solute / volume of the solution in liters
normality = 0.7756 eq / 0.13163 L
normality ≈ 5.892 N
Therefore, the normality of the solution is approximately 5.892 N.
To find the answers to these questions, we need to use some basic formulas and equations related to these concepts. Let's go step by step:
1. Molality (m):
Molality is defined as the number of moles of solute per kilogram of solvent. To calculate molality, we need to find the number of moles of H2SO4 and the mass of water in kilograms.
First, let's find the number of moles of H2SO4:
To do this, we divide the given mass of H2SO4 by its molar mass.
The molar mass of H2SO4 can be calculated by summing the atomic masses of its constituent elements:
H = 1 g/mol
S = 32 g/mol
O = 16 g/mol
4 atoms of Oxygen (O) in H2SO4, so 16 * 4 = 64 g/mol
Now, we can calculate the molar mass of H2SO4:
Molar mass of H2SO4 = (2 * 1) + 32 + (4 * 16) = 98 g/mol
Number of moles of H2SO4 = mass of H2SO4 / molar mass of H2SO4
Number of moles of H2SO4 = 38 g / 98 g/mol
Next, we need to find the mass of water in kilograms.
Given mass of water = 220 g
Mass of water in kilograms = 220 g / 1000 (since there are 1000 grams in a kilogram)
Now we can calculate molality:
Molality (m) = Number of moles of H2SO4 / Mass of Water in kilograms
2. Molarity (M):
Molarity is defined as the number of moles of solute per liter of solution. To calculate molarity, we need to find the number of moles of H2SO4 and the volume of the solution in liters.
Number of moles of H2SO4 is already calculated in step 1.
To find the volume of the solution in liters, we need to use the density of the solution:
Density = Mass / Volume
Rearranging the equation, Volume = Mass / Density
Given density of the solution = 1.96 g/mL
Mass of the solution = mass of H2SO4 + mass of water = 38 g + 220 g
Volume of the solution in liters = (38 g + 220 g) / (1.96 g/mL)
Now we can calculate molarity:
Molarity (M) = Number of moles of H2SO4 / Volume of the solution in liters
3. Mole fraction (X):
Mole fraction is a way to express the composition of a solution in terms of the number of moles of each component. To calculate mole fraction of H2SO4 and water, we need to find the number of moles of each component.
Number of moles of H2SO4 is already calculated in step 1.
Number of moles of water = mass of water / molar mass of water
The molar mass of water (H2O) can be calculated in the same way as in step 1, using the atomic masses of hydrogen (H) and oxygen (O):
Molar mass of water = (2 * 1) + (16 * 1) = 18 g/mol
Now we can calculate the mole fraction of H2SO4 and water:
Mole fraction of H2SO4 = Number of moles of H2SO4 / (Number of moles of H2SO4 + Number of moles of water)
Mole fraction of water = Number of moles of water / (Number of moles of H2SO4 + Number of moles of water)
4. Normality (N):
Normality is a measure of the concentration of a solution based on the number of equivalents of a solute per liter of solution. It is typically used for acid-base reactions. In this case, we can calculate the normality of H2SO4.
Normality (N) is equal to the number of equivalents per liter of solution. For sulfuric acid (H2SO4), each molecule can contribute 2 equivalents of acid.
Number of equivalents of H2SO4 = Number of moles of H2SO4 * number of equivalents per mole
Now we can calculate normality:
Normality (N) = Number of equivalents of H2SO4 / Volume of the solution in liters
Once you have performed the calculations based on the provided information, you will have the values for molality, molarity, mole fraction, and normality of the given solution. Make sure to use the correct units and significant figures when reporting your final answers.