Question

Your chemistry teacher empties her dehumidifier once a day if The composite of the tank is 2 gallons determine how many molecules of water did the dehumidifier collect from the air per millisecond

Answer 1

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

`(2.53 x 10^(26) molecules)/(1 day) x (1 day)/(24 hr) x (1 hr)/(60 min) x (1 min)/(60 sec) x (1 sec)/(1000 msec)`

= 2.93 x 10¹⁸ = 3 x 10¹⁸ molecules/msec

Answer 2

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