Calculate the number of grams of caffeine (C8H10N4O2, molar mass = 194.19g/mol) needed to make 0.20L of a 0.010 M solution. Enter your numerical answer only. Do not include units with your answer. Do pay attention to sig figs.
The Correct Answer and Explanation is :
To calculate the number of grams of caffeine required to make a 0.20 L solution of 0.010 M concentration, follow these steps:
- Calculate the moles of caffeine needed using the formula: Moles=Molarity×Volume\text{Moles} = Molarity \times Volume Where:
- Molarity = 0.010 M
- Volume = 0.20 L
- Convert moles to grams using the molar mass of caffeine: Grams=Moles×Molar Mass\text{Grams} = \text{Moles} \times \text{Molar Mass} Where the molar mass of caffeine (C₈H₁₀N₄O₂) is 194.19 g/mol. Substituting the values: Grams=0.002 moles×194.19 g/mol=0.38838 g\text{Grams} = 0.002 \, \text{moles} \times 194.19 \, \text{g/mol} = 0.38838 \, \text{g}
- Round to the correct number of significant figures: The given values (0.010 M and 0.20 L) each have two significant figures. Therefore, the final answer should also have two significant figures. 0.38838 g→0.39 g0.38838 \, \text{g} \rightarrow 0.39 \, \text{g}
Thus, the number of grams of caffeine needed is 0.39 grams.
Explanation: In this problem, we first use the relationship between molarity (concentration), volume, and moles of solute. By multiplying the molarity of the solution (0.010 M) by the volume of the solution (0.20 L), we determine that we need 0.002 moles of caffeine. We then convert moles into grams using the molar mass of caffeine (194.19 g/mol). The final step is rounding the result to match the appropriate significant figures, ensuring the precision of the result aligns with the given values.