How do I work out how many molecules there are in a #1*g# mass of water?

Question

Henry Antrim · Accepted Answer

#"Do it dimensionally......"#

What do I mean by #"dimensionally"#?

Suppose we have a #1.00*g# mass of water. Now we know that #"Avogadro's number of water molecules"# has a mass of #18.01*g#, and we would typically write this as......

#"Molar mass of water"=18.01*g*mol^-1#

Additionally, I would divide by leaving the UNITS in if I wanted to calculate the MOLAR quantity.

#"Moles of water"=(1.00*g)/(18.01*g*mol^-1)#, and of course we can do some cancellation of units.....

#"Moles of water"=(1.00*cancelg)/(18.01*cancelg*mol^-1)#

#=0.0555*1/(mol^-1)=0.0555*1/(1/(mol))# because #x^-1-=1/x#, and

#=0.0555*1/(mol^-1)=0.0555*1/(1/(mol))=0.0555*mol#.

And as for volumes, we need a #"density"#, #rho#, the which for chemists is typically quoted as #g*mL^-1-=g*cm^-3#.

By definition, #rho="Mass"/"Volume"# i.e. mass per unit volume.

Here #rho_(H_2O)=("Molar quantity"xx"Molar mass")/(1*mL)#

#=(0.0555*cancel(mol)xx18.01*g*cancel(mol^-1))/(1*mL)#

#1*g*mL#; dimensionally consistent as required. Of course, the #"density"# needs to be measured......

You will need to hone your inquiry if this is insufficient assistance.

Serenity Allen · Answer

undefined To work out the number of molecules in a 1 gram mass of water, you can use the following steps:

1. Determine the molar mass of water, which is approximately 18.015 grams per mole (g/mol).
2. Convert the given mass of water (1 gram) to moles by dividing by the molar mass.
3. Use Avogadro's number, which is approximately $6.022 \times 10^{23}$ molecules per mole, to convert moles to molecules.

So, $1 \text{ gram of water} \times \frac{1 \text{ mole}}{18.015 \text{ grams}} \times 6.022 \times 10^{23} \text{ molecules/mole} = \text{ number of molecules in 1 gram of water}$.