The density of water is 1.00 g/mL at 4°C. How many water molecules are present in 2.46 mL of water at this temperature?

Answer 1

#8.23 * 10^(22)#

The idea here is that you need to use the density of water at #4^@"C"# and the volume of the sample to find its mass, then use water's molar mass to find how many moles of water you get in this sample.
So, density is defined as mass per unit of volume. In this case, a density of #"`1.00 g/mL"# tells you that every milliliter of water has a mass of #"1.00 g"#.
This means that #"2.46 mL"# will have a mass of
#2.46color(red)(cancel(color(black)("mL"))) * "1.00 g"/(1color(red)(cancel(color(black)("mL")))) = "2.46 g"#
Now, water has molar mass of #"18.015 g/mol"#. This tells you that every mole of water has mass of #"18.015 g"#. In your case, the sample will contain
#2.46color(red)(cancel(color(black)("g"))) * "1 mole water"/(18.015color(red)(cancel(color(black)("g")))) = "0.1366 moles water"#
Finally, the relationship between number of moles and number of molecules is given by Avogadro's number, which tells you that every mole of a substance contains exactly #6.022 * 20^(23)# molecules of that substance.

This means that you will have

#0.1366color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = color(green)(8.23 * 10^(22)"molecules")#
So, #"2.46 mL"# of water at a temperature of #4^@"C"# wil contain a total of #8.23 * 10^(22)# molecules of water.
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Answer 2

To find the number of water molecules in 2.46 mL of water at 4°C, we use the formula:

Number of molecules = (Volume of water in mL) * (Density of water in g/mL) * (Avogadro's number) / (Molar mass of water in g/mol)

Number of molecules = (2.46 mL) * (1.00 g/mL) * (6.022 × 10^23 molecules/mol) / (18.015 g/mol)

Number of molecules ≈ 8.25 × 10^22 molecules

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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