You need 550. mL of a 4.9% (m/v) glucose solution. If you have a 23 % (m/v) glucose solution on hand, how many milliters of this solution do you need?
Express your answer to two significant figures and include the appropriate units.
To find the amount of the 23% (m/v) glucose solution needed, we can set up a proportion. Let x be the number of milliliters of the 23% solution needed.
(23 g glucose / 100 mL solution) = (4.9 g glucose / 550 mL solution)
Cross-multiplying, we get:
23 g glucose * 550 mL solution = 4.9 g glucose * x mL solution
Simplifying, we find:
12650 g·mL = 4.9 g·mL·x
Dividing both sides by 4.9 g·mL, we get:
(12650 g·mL) / (4.9 g·mL) = x
x ≈ 2580 mL
Therefore, you need approximately 2580 mL of the 23% (m/v) glucose solution.
To determine the volume of the 23% glucose solution needed, we can set up a proportion based on the amount of glucose in each solution.
Let's assign the following variables:
x = volume of the 23% glucose solution needed (in milliliters)
We can set up the following proportion:
23% / 100% = x mL / 550 mL
To solve for x, we can cross multiply and then divide by 23:
x = (23 / 100) * 550 mL
x ≈ 126.5 mL
Therefore, you would need approximately 126.5 mL of the 23% glucose solution.
To solve this problem, we can use the equation:
(C1)(V1) = (C2)(V2)
where C1 is the concentration of the starting solution, V1 is the volume of the starting solution, C2 is the concentration of the desired solution, and V2 is the volume of the desired solution.
In this case:
C1 = 23% (m/v) = 0.23 (since the concentration is expressed as a decimal)
C2 = 4.9% (m/v) = 0.049
V2 = 550 mL
We can rearrange the equation to solve for V1:
V1 = (C2)(V2) / C1
Plugging in the values:
V1 = (0.049)(550 mL) / 0.23
V1 ≈ 117.4 mL
Therefore, you would need approximately 117.4 mL of the 23% glucose solution.