Question

On a hot summer day Mr. Little went for a swim. Since his pool needed to be filled, he turned the hose on and went to Target. He calculated that his pool could add 234000 mL of water before overflowing. When he returned, he determined that he added about 8.94 x 10^25 molecules of water. Determine the number of mL of water he added to the pool and indicate if the pool overflowed or not. Must use dimensional analysis.

Answer 1

The volume = 8.94 x 10^25/3.346 x 10^22 =2671.85 mL

Thus, the volume of water added (2671.85 mL) is considerably less than the calculated volume (234000 mL). The pool will not overflow.

Step-by-step explanation:

The volume of water added to the pool can be calculated using the formula below:

Number of molecules (molecules)= N (molecules/mol)*density (g/mL)*volume (mL)/molar mass (g/mol)

Where:

N is the Avogadro constant and it is equal to 6.022 x 10^23, the density of water is 1 g/mL, and molar mass of water is 18 g/mol. In the given problem, 8.94 x 10^25 molecules of water was added, using the formula above:

8.94 x 10^25 = 6.022 x 10^23*1*volume/18

Therefore, volume = 8.94 x 10^25/3.346 x 10^22 =2671.85 mL

Thus, the volume of water added (2671.85 mL) is considerably less than the calculated volume (234000 mL). The pool will not overflow.