Final answer:
To convert 1 x 10^23 molecules of Mg(C2H3O2)2 to grams, calculate the molar mass of Mg(C2H3O2)2 and use Avogadro's number to find the fraction of a mole represented by 1 x 10^23 molecules. Multiply this fraction by the molar mass to get the mass in grams, which is approximately 23.72 grams.
Step-by-step explanation:
To convert 1 x 1023 molecules of Mg(C2H3O2)2 to grams, you first need to determine the molar mass of Mg(C2H3O2)2. This is done by adding the atomic masses of magnesium (Mg), carbon (C), hydrogen (H), and oxygen (O) based on their respective quantities in the molecular formula. Using the periodic table:
Add these up to get the molar mass of Mg(C2H3O2)2, which is approximately 142.33 g/mol. The number 1 x 1023 is close to Avogadro's number, which is 6.022 x 1023. Thus, you have approximately 1/6 of a mole of Mg(C2H3O2)2, because the number of molecules you have is 1/6 of Avogadro's number. Finally, to find the mass in grams, multiply the fraction of a mole (approximately 1/6) by the molar mass of Mg(C2H3O2)2.
This results in: (1/6) x 142.33 g/mol ≈ 23.72 grams. Therefore, 1 x 1023 molecules of Mg(C2H3O2)2 is approximately 23.72 grams.