Answer :
To determine how a scientist can make two solutions with the same molarity, let's first understand what molarity is. Molarity (M) is defined as the number of moles of solite dissolved per liter of solution. The formula for molarity is:
[tex]\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Given this definition, let's consider each option:
Option A: By dissolving the same number of grams of each substance in the same volume of water.
The number of grams does not directly correlate to the number of moles unless the substances have the same molar mass. Different substances have different molar masses, so dissolving the same number of grams of different substances usually results in different molarities. Therefore, this option is incorrect.
Option B: By dissolving 1 mole of each substance in enough water to make sure dissolving is complete.
While dissolving 1 mole of each substance ensures that the same number of moles is used, the volumes of the resulting solutions might not be the same if the goal is just to ensure complete dissolution. Different volumes lead to different molarities, so this option does not guarantee the same molarity. Therefore, this option is also incorrect.
Option C: By dissolving the maximum amount of each substance in the same volume of water.
Maximum solubility varies for different substances. This means that dissolving the maximum amount of each substance would yield different moles of solute in the same volume of water, leading to different molarities. Thus, this option is incorrect.
Option D: By dissolving the same number of moles of each substance in the same volume of water.
This option ensures that the ratio of moles of solute to liters of solution is the same for both substances. Since molarity is essentially this ratio, dissolving the same number of moles of each substance in the same volume of water guarantees that both solutions will have the same molarity. Thus, this option is correct.
Therefore, the correct answer is:
D. By dissolving the same number of moles of each substance in the same volume of water.
[tex]\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Given this definition, let's consider each option:
Option A: By dissolving the same number of grams of each substance in the same volume of water.
The number of grams does not directly correlate to the number of moles unless the substances have the same molar mass. Different substances have different molar masses, so dissolving the same number of grams of different substances usually results in different molarities. Therefore, this option is incorrect.
Option B: By dissolving 1 mole of each substance in enough water to make sure dissolving is complete.
While dissolving 1 mole of each substance ensures that the same number of moles is used, the volumes of the resulting solutions might not be the same if the goal is just to ensure complete dissolution. Different volumes lead to different molarities, so this option does not guarantee the same molarity. Therefore, this option is also incorrect.
Option C: By dissolving the maximum amount of each substance in the same volume of water.
Maximum solubility varies for different substances. This means that dissolving the maximum amount of each substance would yield different moles of solute in the same volume of water, leading to different molarities. Thus, this option is incorrect.
Option D: By dissolving the same number of moles of each substance in the same volume of water.
This option ensures that the ratio of moles of solute to liters of solution is the same for both substances. Since molarity is essentially this ratio, dissolving the same number of moles of each substance in the same volume of water guarantees that both solutions will have the same molarity. Thus, this option is correct.
Therefore, the correct answer is:
D. By dissolving the same number of moles of each substance in the same volume of water.
