Given data:
Amount of water collected in the dehumidifier= 2 gallons
Time taken to collect 2 gallons = 1 day
Calculation
Step1 : Find the mass of 2 gallons of water
1 gallon = 3.79 L
Therefore, 2 gallons = 2 gallon * 3.79 L/1 gallon = 7.58 L
Density of water = 1 kg/L
Therefore, Mass of 7.58 L water = Density * Vol = 1 * 7.58 = 7.58 kg = 7580 g
Step 2: Convert mass of water to molecules
1 mole of water = 18 g = 6.023 *10^23 molecules
therefore, 7580 g contains: 6.023 * 10^23 * 7580/18 = 2.536 *10^26 molecules
Step 3: Calculate the molecules of water collected/millisecond
Now,
2.536*10^26 water molecules are collected in 1 day
1 day = 24 hrs * 60 min * 60 sec = 86400 sec
10^-3 sec = 1 millisec
therefore, 86400 sec = 1 millisec * 86400 sec/10^-3 sec = 8.64 * 10^7 millisec
Thus water molecules collected/millisec = 2.536*10^26/8.64*10^7
= 2.935 *10^32 molecules/millisec
Volume of water = 2 gal
1 gal = 3.78 L
2 gal = 7.56 L = 7600 ml
Density of water = 1 g/ml
Mass of water = 7600 ml x 1 g/ml = 7600 g
Molar mass of water = 18g/mol
Mole of water = mass of water / molar mass of water = 7600 g/18g/mol = 420 moles
According to Avogadro, 1 mole of water = 6.023 x 10²³ molecules of water
Number of water molecules = 420 x 6.023 x 10²³= 2529.66 x 10²³molecules
Molecules of water collected in 1 day = 2.53 x 10²⁶
[tex]\frac{2.53 x 10^{26} molecules}{1 day} x \frac{1 day}{24 hr} x \frac{1 hr}{60 min} x \frac{1 min}{60 sec} x \frac{1 sec}{1000 msec}[/tex]
= 2.93 x 10¹⁸ = 3 x 10¹⁸ molecules/msec
