A biochemist carefully measures the molarity of sucrose in 70.7mL of cell growth medium to be 96.5 mM.Unfortunately, a careless graduate student forgets to cover the container of growth medium and a substantial amount of the solvent evaporates. The volume of the cell growth medium falls to 28.3mL. Calculate the new molarity of sucrose in the cell growth medium.Round each of your answers to 3 significant digits.
Question
A biochemist carefully measures the molarity of sucrose in 70.7mL of cell growth medium to be 96.5 mM.Unfortunately, a careless graduate student forgets to cover the container of growth medium and a substantial amount of the solvent evaporates. The volume of the cell growth medium falls to 28.3mL. Calculate the new molarity of sucrose in the cell growth medium.Round each of your answers to 3 significant digits.
Solution
The molarity of a solution is defined as the number of moles of solute per liter of solution. In this case, the solute is sucrose and the solvent is the cell growth medium.
Step 1: Convert the initial volume of the solution from mL to L.
70.7 mL = 0.0707 L
Step 2: Calculate the initial number of moles of sucrose in the solution using the initial molarity and volume.
Number of moles = Molarity x Volume Number of moles = 96.5 mM x 0.0707 L = 6.82 mmol
Step 3: Convert the final volume of the solution from mL to L.
28.3 mL = 0.0283 L
Step 4: Calculate the final molarity of the solution using the number of moles of sucrose and the final volume.
Final Molarity = Number of moles / Final Volume Final Molarity = 6.82 mmol / 0.0283 L = 241 mM
So, the new molarity of sucrose in the cell growth medium is 241 mM.
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