____?____g of glucose C6H12O6 must be dissolved in 400 g of water to give a solution that is 0.258 m(molality).
You know molality = # mols/kg solvent. Rearrange that to # mols = molality x kg solvent. Call that equation 1.
You know # mols = grams/molar mass. Call that equation 2.
Now set # mols in equation 1 = # mols in equation 2 and substitute.
molality x kg solvent = g/molar mass OR
molality x kg solvent x molar mass = grams.
You have molality desired, kg solvent, and molar mass. Solve for grams.
Post your work if you get stuck.
kg solvent x molality x molar mass = grams.
Here is variation of the method offered by DrBob:
0.258m means 0.258 moles / kg of water. Based on that we can set up and solve for x:
**0.258 mol/1 kg = x / 0.400 kg
[Note: 400g = 0.400 kg]
**Solving for x gives us the moles of glucose to be used.
**Calculate the molar mass of C6H12O6 and multiply it by the value of "x" to get the grams of glucose to be added to the 400g of water.
thanks i got it
To find the mass of glucose that must be dissolved in water, we need to use the equation for molality:
Molality (m) = moles of solute / mass of solvent (kg)
First, we need to convert the given mass of water to kilograms. Since 1 kg = 1000 g, the mass of water in kilograms is:
Mass of water = 400 g / 1000 = 0.4 kg
Now, we can rearrange the equation to solve for moles of solute:
Moles of solute = Molality × Mass of solvent (kg)
Given that the molality (m) is 0.258 and the mass of water (solvent) is 0.4 kg, we can substitute these values into the equation:
Moles of solute = 0.258 × 0.4 = 0.1032 mol
The molecular formula of glucose (C6H12O6) tells us that it has 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Thus, the molar mass of glucose is:
Molar mass of glucose = (6 × atomic mass of carbon) + (12 × atomic mass of hydrogen) + (6 × atomic mass of oxygen)
Using the atomic masses from the periodic table:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Oxygen (O): 16.00 g/mol
Molar mass of glucose = (6 × 12.01) + (12 × 1.01) + (6 × 16) = 72.06 + 12.12 + 96 = 180.18 g/mol
Finally, we can use the moles of solute and the molar mass of glucose to find the mass of glucose:
Mass of glucose = Moles of solute × Molar mass of glucose
Mass of glucose = 0.1032 mol × 180.18 g/mol
Calculating this gives us the mass of glucose needed to be dissolved in water:
Mass of glucose = 18.56 g
Therefore, 18.56 grams of glucose (C6H12O6) must be dissolved in 400 grams of water to give a solution that is 0.258 m(molality).