A student placed 13.5g of glucose (\rm C_6H_{12}O_6) in a volumetric flask, added enough water to dissolve the glucose by swirling, then carefully added additional water until the 100. \rm mL mark on the neck of the flask was reached. The flask was then shaken until the solution was uniform. A 60.0 \rm mL sample of this glucose solution was diluted to 0.500 \rm L. How many grams of glucose are in 100. \rm mL of the final solution?
1.62
To calculate the amount of glucose in 100 mL of the final solution, we first need to determine the concentration of glucose in the original solution.
Given that 13.5 g of glucose was dissolved in enough water to reach the 100 mL mark on the volumetric flask, we can calculate the concentration as follows:
Concentration = Mass of solute / Volume of solution
Concentration = 13.5 g / 100 mL
To convert mL to L, we divide by 1000:
Concentration = 13.5 g / (100 mL * (1 L / 1000 mL))
Concentration = 13.5 g / 0.1 L
Concentration = 135 g/L
Now that we know the concentration of glucose in the original solution is 135 g/L, we can calculate the amount of glucose in 60.0 mL of this solution by multiplying the concentration by the volume:
Amount of glucose in 60.0 mL = Concentration * Volume
Amount of glucose in 60.0 mL = 135 g/L * 60.0 mL
To convert mL to L, we divide by 1000:
Amount of glucose in 60.0 mL = 135 g/L * (60.0 mL * (1 L / 1000 mL))
Amount of glucose in 60.0 mL = 135 g/L * 0.06 L
Amount of glucose in 60.0 mL = 8.1 g
Finally, to calculate the amount of glucose in 100 mL of the final solution, we can use the concept of proportional relationships since the amount of glucose is directly proportional to the volume of the solution:
Amount of glucose in 100 mL = (Amount of glucose in 60.0 mL / 60.0 mL) * 100 mL
Amount of glucose in 100 mL = (8.1 g / 60.0 mL) * 100 mL
Amount of glucose in 100 mL = 13.5 g
Therefore, there are 13.5 grams of glucose in 100 mL of the final solution.