5.0 x 10^24 molecules = ____ liters (5 times ten to the 24th power molecules is equal to how many liters?)

2 Answers

crmhaske's profile pic

crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

The answer depends on the substance in question.  For the sake of demonstration I will use pure water:

The first step is to determine how many moles there are.  To do that we use Avagadro's number which is how many molecules there are per mole.  The number is: 6.02×10^23 /mol.

To determined how many moles we have from the number of molecules we divide the number of molecules by Avagadro's number:

(5.0 x 10^24) / (6.02×10^23) = 8.3 mol

Next we can determine how many grams of water we have based on the molar mass of water.

Water is H20 so the molar mass of water = 2 times the molar mass of hydrogen plus the molar mass of oxygen.

molar mass hydrogen = 1.00794 g/mol
molar mass oxygen = 15.9994 g/mol
molar mass water =  2*(1.00794) + 15.9994 = 18.02 g/mol

Next to determine the number of grams of water we have we multiply the molar mass of water by the number of total moles:

Grams of water = 18.02 * 8.3 = 149.57 g

For water 1 g = 1mL therefore we have 149.57mL of water or 0.15L

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

In case of water the litre  for 5*10^24 molecules  is calculated.

One mole of  of water( H2O ) molecules has the mass  = (2+16 )gm.

Therefore one litre  or 1000 cc of water with 1000 gm mass has = 1000/18 = 55.5555... mole of water molecules.

So  5*10^24 moles  of water has (5*10^24 / Avogodro number ) moles = 5*10^24/(6.022*10^23) moles = 50/6.022 moles = 8.302889404 moles.

= 8.30289404/55.555555.. litres of water.

= 0.149452009 litre of water.