Answer:
Step-by-step explanation:
1.To convert 7.74 x 10^26 molecules of cesium nitrate to moles, we need to use Avogadro’s number, which is 6.022 x 10^23 molecules per mole. We can set up the following conversion factor:
1 mole / (6.022 x 10^23 molecules)
This conversion factor allows us to cancel out the units of molecules and convert to moles. Multiplying the given quantity by this conversion factor, we get:
7.74 x 10^26 molecules x (1 mole / 6.022 x 10^23 molecules)
= 128.5 moles (rounded to three significant figures)
Therefore, 7.74 x 10^26 molecules of cesium nitrate is equal to 128.5 moles of cesium nitrate.
2.To convert 58.0 grams of magnesium nitrate to moles, we need to use the molar mass of magnesium nitrate.
The molar mass of magnesium nitrate can be calculated by summing the atomic masses of its constituent elements, which are:
Magnesium (Mg): 24.31 g/mol
Nitrogen (N): 14.01 g/mol
Oxygen (O) (3 atoms): 3 x 16.00 g/mol = 48.00 g/mol
So the molar mass of magnesium nitrate (Mg(NO3)2) is:
24.31 g/mol (Mg) + 2 x (14.01 g/mol (N) + 3 x 16.00 g/mol (O)) = 148.31 g/mol
We can use this molar mass as a conversion factor to convert grams of magnesium nitrate to moles. The conversion factor is:
1 mole / 148.31 grams
So, we can calculate the number of moles of magnesium nitrate as follows:
58.0 grams x (1 mole / 148.31 grams) = 0.391 moles
Therefore, 58.0 grams of magnesium nitrate is equal to 0.391 moles of magnesium nitrate.