How many of vat dye are needed to make a 500mL solution with a mass concentration of 0.1g/mL?

To calculate the amount of vat dye needed to make a 500mL solution with a mass concentration of 0.1g/mL, you would multiply the volume of the solution by the desired concentration.

Amount of vat dye = Volume of solution x Concentration
Amount of vat dye = 500mL x 0.1g/mL
Amount of vat dye = 50g

Therefore, you would need 50g of vat dye to make a 500mL solution with a mass concentration of 0.1g/mL.

Step 1: Calculate the mass of vat dye needed

Mass = Concentration x Volume
Mass = 0.1 g/mL x 500 mL
Mass = 50 g

Step 2: Convert mass to number of moles

Moles = Mass / Molar mass
Assuming the molar mass of the vat dye is 250 g/mol:
Moles = 50 g / 250 g/mol
Moles = 0.2 mol

Step 3: Determine the number of vat dye molecules

Since each mole contains 6.022 x 10^23 molecules (Avogadro's number):
Number of molecules = Moles x Avogadro's number
Number of molecules = 0.2 mol x 6.022 x 10^23 molecules/mol
Number of molecules = 1.2044 x 10^23 molecules

Therefore, approximately 1.2044 x 10^23 molecules of vat dye are needed to make a 500mL solution with a mass concentration of 0.1g/mL.