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Complete the analogy: Blueprint is to architect as algorithm is to ______.
An architect uses a blueprint to design a building. Similarly, a programmer uses an algorithm to design a computer program. While engineers and mathematicians also use algorithms, the closest analogy is with a programmer.
At the point of precipitation: $[\text{Ba}^{2+}][\text{SO}_4^{2-}] = K_{sp} = 1 \times 10^{-10}$
Find $[\text{SO}_4^{2-}]$ in the final mixture:
Moles of SO$_4^{2-}$ added $= 0.050\ \text{L} \times 1\ \text{M} = 0.05\ \text{mol}$
Final volume $= 500\ \text{mL} = 0.5\ \text{L}$
$[\text{SO}_4^{2-}]_{\text{final}} = \dfrac{0.05}{0.5} = 0.1\ \text{M}$
Find $[\text{Ba}^{2+}]$ in the final mixture:
$[\text{Ba}^{2+}]_{\text{final}} = \dfrac{K_{sp}}{[\text{SO}_4^{2-}]} = \dfrac{1\times10^{-10}}{0.1} = 1\times10^{-9}\ \text{M}$
Back-calculate original concentration: Final volume is 10× original Ba$^{2+}$ volume (500 mL total, 450 mL original solution).
Original $[\text{Ba}^{2+}] = 1\times10^{-9} \times \dfrac{500}{450} \approx \mathbf{2\times10^{-9}}\ \text{M}$
The change in time is given by $\Delta t = \frac{1}{2} \alpha \Delta \theta \times t$.
- $12 = \frac{1}{2} \alpha (40 - \theta) \times 86400$
- $-4 = \frac{1}{2} \alpha (20 - \theta) \times 86400$
- Dividing the equations gives $\theta = 25^{\circ}\text{C}$.
- Substituting $\theta$ back gives $\alpha = 1.85 \times 10^{-5}/^{\circ}\text{C}$.
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