how many grams of Na2CO3 must be dissolved into 155 g of water to create a solution with the molality of 8.20 mol/kg?
To calculate the grams of Na2CO3 needed to create a solution with the given molality, you need to follow these steps:
Step 1: Convert the given mass of water to kg.
Mass of water = 155 g
Mass of water = 155 g * (1 kg / 1000 g)
Mass of water = 0.155 kg
Step 2: Calculate the moles of solute (Na2CO3) required using the molality formula.
Molality (m) = moles of solute / mass of solvent (in kg)
Rearrange the formula to solve for moles of solute:
Number of moles of solute = molality * mass of solvent (in kg)
Number of moles of solute = 8.20 mol/kg * 0.155 kg
Number of moles of solute = 1.271 mol
Step 3: Calculate the molar mass of Na2CO3.
The molar mass of Na2CO3 = (2 * molar mass of Na) + molar mass of C + (3 * molar mass of O)
Molar mass of Na = 22.99 g/mol
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of Na2CO3 = (2 * 22.99 g/mol) + 12.01 g/mol + (3 * 16.00 g/mol)
Molar mass of Na2CO3 = 105.99 g/mol
Step 4: Calculate the mass of Na2CO3 required using the moles of solute and molar mass.
Mass of Na2CO3 = Number of moles of solute * Molar mass of Na2CO3
Mass of Na2CO3 = 1.271 mol * 105.99 g/mol
Mass of Na2CO3 ≈ 134.9 g
Therefore, approximately 134.9 grams of Na2CO3 must be dissolved into 155 grams of water to create a solution with a molality of 8.20 mol/kg.
To determine the number of grams of Na2CO3 needed to create a solution with a molality of 8.20 mol/kg, we need to follow a few steps:
Step 1: Calculate the number of moles of Na2CO3 required.
- Molality (m) is defined as the number of moles of solute per kilogram of solvent.
- We are given the molality, which is 8.20 mol/kg.
- Since we know the molality and the mass of the solvent (water), we can calculate the moles of Na2CO3 required.
- The given mass of water is 155 g.
To find moles, we need to multiply the molality by the mass of solvent (in kg). Converting the mass of water from grams to kilograms:
Mass of water (in kg) = 155 g / 1000 = 0.155 kg
Number of moles of Na2CO3 required = Molality x Mass of water (in kg)
= 8.20 mol/kg x 0.155 kg
Step 2: Calculate the molar mass of Na2CO3.
- Na2CO3 contains two sodium atoms (Na), one carbon atom (C), and three oxygen atoms (O).
- Sodium has a molar mass of 22.99 g/mol.
- Carbon has a molar mass of 12.01 g/mol.
- Oxygen has a molar mass of 16.00 g/mol.
Molar mass of Na2CO3 = (2 x Molar mass of Na) + Molar mass of C + (3 x Molar mass of O)
= (2 x 22.99 g/mol) + 12.01 g/mol + (3 x 16.00 g/mol)
Step 3: Calculate the grams of Na2CO3 required.
- To get the grams of Na2CO3 required, we need to multiply the number of moles obtained in Step 1 by the molar mass of Na2CO3 obtained in Step 2.
Grams of Na2CO3 required = Number of moles of Na2CO3 required x Molar mass of Na2CO3
Now it's time to plug in the calculated values to find the grams of Na2CO3 required.
MW(Na2CO3)=105.96g/mol
Volume- 155g H20 = 0.155L H20
Concentration- 8.20mol/L
n=CV
n=(8.20mol/L)(0.155L)
n=52.9mol
m=nMW
m=(52.9mol)(105.96g/mol)
m=5605.6g
m=5.61Kg