Exercise Here's a balanced chemical equation for a reaction that occurs in the body to metabolize glucose: C_(6)H_(12)O_(6)+6O_(2)arrow 6CO_(2)+6H_(2)O How many grams are needed to produce 100 g carbon dioxide? (M_(cose)=44.01g/molMMCC_(6)H_(12)O_(6))=180.16g/mol)

To find out how many grams of glucose are needed to produce 100 grams of carbon dioxide, we need to use the balanced chemical equation provided:<br /><br />$C_{6}H_{12}O_{6} + 6O_{2} \rightarrow 6CO_{2} + 6H_{2}O$<br /><br />From the equation, we can see that 1 mole of glucose ($C_{6}H_{12}O_{6}$) produces 6 moles of carbon dioxide ($CO_{2}$).<br /><br />First, let's calculate the moles of carbon dioxide produced from 100 grams:<br /><br />Moles of $CO_{2}$ = $\frac{100 \text{ g}}{44.01 \text{ g/mol}} \approx 2.27 \text{ moles}$<br /><br />Since 1 mole of glucose produces 6 moles of carbon dioxide, we need to find out how many moles of glucose are required to produce 2.27 moles of carbon dioxide:<br /><br />Moles of glucose needed = $\frac{2.27 \text{ moles}}{6} \approx 0.378 \text{ moles}$<br /><br />Now, let's convert the moles of glucose to grams using the molar mass of glucose (180.16 g/mol):<br /><br />Grams of glucose needed = $0.378 \text{ moles} \times 180.16 \text{ g/mol} \approx 68.27 \text{ g}$<br /><br />Therefore, approximately 68.27 grams of glucose are needed to produce 100 grams of carbon dioxide.