2) How many grams is 5.0times 10^30 molecules of table sugar (C_(12)H_(22)O_(11)). SHOW WORK FOR CREDIT BOXIN ANSWER

To find the mass of $5.0\times 10^{30}$ molecules of table sugar $(C_{12}H_{22}O_{11})$, we need to follow these steps:<br /><br />1. Calculate the molar mass of table sugar $(C_{12}H_{22}O_{11})$.<br />2. Convert the number of molecules to moles.<br />3. Calculate the mass of the sugar in grams.<br /><br />Step 1: Calculate the molar mass of table sugar $(C_{12}H_{22}O_{11})$.<br /><br />The molar mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and oxygen (O) is 16.00 g/mol.<br /><br />Molar mass of $C_{12}H_{22}O_{11}$ = (12 * 12.01 g/mol) + (22 * 1.01 g/mol) + (11 * 16.00 g/mol)<br />Molar mass of $C_{12}H_{22}O_{11}$ = 144.12 g/mol + 22.22 g/mol + 176.00 g/mol<br />Molar mass of $C_{12}H_{22}O_{11}$ = 342.34 g/mol<br /><br />Step 2: Convert the number of molecules to moles.<br /><br />We know that 1 mole of any substance contains Avogadro's number of molecules, which is $6.022\times 10^{23}$ molecules.<br /><br />Number of moles = Number of molecules / Avogadro's number<br />Number of moles = $5.0\times 10^{30}$ molecules / $6.022\times 10^{23}$ molecules/mol<br />Number of moles = $8.30\times 10^{6}$ moles<br /><br />Step 3: Calculate the mass of the sugar in grams.<br /><br />Mass = Number of moles * Molar mass<br />Mass = $8.30\times 10^{6}$ moles * 342.34 g/mol<br />Mass = $2.85\times 10^{9}$ grams<br /><br />Therefore, $5.0\times 10^{30}$ molecules of table sugar $(C_{12}H_{22}O_{11})$ is equivalent to $2.85\times 10^{9}$ grams.