Final answer:
To prepare a 0.50% (w/w) concentration of glucose solution with 655 g of water, approximately 3.275 g of glucose needs to be added, corresponding to option (a).
Step-by-step explanation:
The question asks how many grams of glucose must be added to 655 g of water to prepare a 0.50% (w/w) concentration of a glucose solution. To calculate this, we need to understand that a 0.50% concentration means that there are 0.50 grams of glucose for every 100 grams of the solution.
First, let's find the total mass of the solution. Since the concentration is based on weight/weight percentage, we consider the weight of the water and the glucose together:
- Total mass of the solution = Mass of water + Mass of glucose
As per the 0.50% concentration:
- 0.50 g of glucose / 100 g of solution = Mass of glucose / (655 g water + Mass of glucose)
Let's solve for Mass of glucose:
Cross-multiply and rearrange the equation:
- 0.50 x (655 g + Mass of glucose) = 100 x Mass of glucose
- 327.5 g + 0.50 x Mass of glucose = 100 x Mass of glucose
- 327.5 g = 99.5 x Mass of glucose
- Mass of glucose = 327.5 / 99.5
- Mass of glucose ≈ 3.29 g
The closest answer to this calculation is 3.275 g, which is option (a).