A 40% glucose solution (by mass) has a density of 1.149 g/mL. What volume of this solution would provide 25.4 g of glucose?
Oh, glucose solutions, sweet! Looks like we've got a puzzle to solve here. Let's break it down step by step!
First, we need to find the mass of the glucose solution. Since we know that the density is 1.149 g/mL, we can use this to calculate the mass.
Given that density = mass/volume, we can rearrange the equation to find the mass:
mass = density * volume
Now, we know that the solution is 40% glucose by mass, so the remaining 60% must be the solvent. We can use this information to calculate the mass of the glucose in the solution.
mass of glucose = 40% * mass of solution
Now, since we're given that the mass of glucose is 25.4 g, we can solve for the mass of the solution using the equation above.
25.4 g = 0.4 * mass of solution
Dividing both sides by 0.4, we find:
mass of solution = 25.4 g / 0.4
Mass of solution = 63.5 g
Now that we know the mass of the solution, we can find the volume. We can use the equation we found earlier:
mass = density * volume
volume = mass / density
Plugging in the values we have:
volume = 63.5 g / 1.149 g/mL
Calculating this value, we find:
volume ≈ 55.23 mL
So, to obtain 25.4 g of glucose, you would need a volume of approximately 55.23 mL of the 40% glucose solution. Time to mix and pour the glucose!
To find the volume of the 40% glucose solution that would provide 25.4 g of glucose, we need to use the information given about the density and the mass percent.
First, let's determine the mass of the solution. Since we know that 40% of the solution's mass is glucose, we can calculate the mass of the solution using the equation:
Mass of Solution = Mass of Glucose / Mass Percent of Glucose
Substituting the given values:
Mass of Solution = 25.4 g / 0.4 = 63.5 g
Next, we can use the density of the solution to find its volume. The relationship between density, mass, and volume is:
Density = Mass / Volume
Rearranging the equation to solve for volume:
Volume = Mass / Density
Substituting the known values:
Volume = 63.5 g / 1.149 g/mL ≈ 55.26 mL
Therefore, approximately 55.26 mL of the 40% glucose solution would provide 25.4 g of glucose.