Which of the following graphs best represents the relationship between the amount of solute (in moles) and the volume of solution (in liters) for a solution with constant molarity?
A
A horizontal line above the x-axis
B
A curve that increases exponentially
C
A straight line passing through the origin
D
A straight line parallel to the y-axis
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1
Recall the definition of molarity (M), which is the concentration of a solution expressed as moles of solute per liter of solution. It is given by the formula:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
Rearrange the formula to express the moles of solute in terms of molarity and volume:
\[ \text{moles of solute} = M \times \text{volume of solution} \]
Since the molarity (M) is constant, the relationship between moles of solute and volume is a direct proportionality, meaning the moles increase linearly as volume increases.
A direct proportionality between two variables is represented graphically by a straight line passing through the origin (0,0), because when the volume is zero, the moles of solute must also be zero.
Therefore, the graph that best represents this relationship is a straight line passing through the origin, with the slope equal to the constant molarity.