정답: $5$

ㄱ. 용질$(\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(s))(\backslash mathrm\{NaOH\}(s))$의 질량은 $10\mathrm{g}10\backslash ,\backslash mathrm\{g\}$, 용매(물)의 질량은 $1\mathrm{k}\mathrm{g}=1\backslash ,\backslash mathrm\{kg\}\; =\{\}$$1\times 10^3\mathrm{g}=1\; \backslash times\; 10^\{3\}\backslash ,\backslash mathrm\{g\}\; =\{\}$$1000\mathrm{g}1000\backslash ,\backslash mathrm\{g\}$이므로
용액$(\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(aq))(\backslash mathrm\{NaOH\}(aq))$의 질량은 $10\mathrm{g}+1000\mathrm{g}=1010\mathrm{g}10\backslash ,\backslash mathrm\{g\}\; +\; 1000\backslash ,\backslash mathrm\{g\}\; =\; 1010\backslash ,\backslash mathrm\{g\}$이다.
그러므로 퍼센트 농도는 ${\displaystyle \frac{10\mathrm{g}}{1010\mathrm{g}}}\times 100\mathrm{\%}={\displaystyle \frac{100}{101}}\mathrm{\%}\backslash dfrac\{10\backslash ,\backslash mathrm\{g\}\}\{1010\backslash ,\backslash mathrm\{g\}\}\; \backslash times\; 100\backslash ,\backslash \%\; =\; \backslash dfrac\{100\}\{101\}\backslash ,\backslash \%$이다. (O)

ㄴ. $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\backslash mathrm\{NaOH\}$의 화학식량은 $4040$이므로 용질$(\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(s))(\backslash mathrm\{NaOH\}(s))$의 몰 수는 $10\mathrm{g}\times {\displaystyle \frac{1}{40\mathrm{g}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}}}={\displaystyle \frac{1}{4}}\mathrm{m}\mathrm{o}\mathrm{l}10\backslash ,\backslash mathrm\{g\}\; \backslash times\; \backslash dfrac\{1\}\{40\backslash ,\backslash mathrm\{g/mol\}\}\; =\; \backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{mol\}$이다.
이때 용액의 부피는 $1\mathrm{L}1\backslash ,\backslash mathrm\{L\}$이므로 몰 농도는 ${\displaystyle \frac{{\displaystyle \frac{1}{4}}\mathrm{m}\mathrm{o}\mathrm{l}}{1\mathrm{L}}}=\backslash dfrac\{\backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{mol\}\}\{1\backslash ,\backslash mathrm\{L\}\}\; =\{\}$${\displaystyle \frac{1}{4}}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{L}=\backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{mol/L\}\; =\{\}$${\displaystyle \frac{1}{4}}\mathrm{M}\backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{M\}$이다. (O)

ㄷ. 용질$(\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(s))(\backslash mathrm\{NaOH\}(s))$의 몰 수는 ${\displaystyle \frac{1}{4}}\mathrm{m}\mathrm{o}\mathrm{l}\backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{mol\}$이고, 용매(물)의 질량은 $1\mathrm{k}\mathrm{g}1\backslash ,\backslash mathrm\{kg\}$이므로
몰랄 농도는 ${\displaystyle \frac{{\displaystyle \frac{1}{4}}\mathrm{m}\mathrm{o}\mathrm{l}}{1\mathrm{k}\mathrm{g}}}=\backslash dfrac\{\backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{mol\}\}\{1\backslash ,\backslash mathrm\{kg\}\}\; =\{\}$${\displaystyle \frac{1}{4}}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{k}\mathrm{g}=\backslash dfrac\{1\}\{4\}\backslash ,\backslash mathrm\{mol/kg\}\; =\{\}$${\displaystyle \frac{1}{4}}m\backslash dfrac\{1\}\{4\}\backslash ,m$이다. (O)

따라서 답은 $55$번이다.

정답: $1$

$\text{몰 농도}(\mathrm{M})={\displaystyle \frac{\text{용질의 몰 수}(\mathrm{m}\mathrm{o}\mathrm{l})}{\text{용액의 부피}(\mathrm{L})}}\backslash text\{몰\; 농도\}(\backslash mathrm\{M\})\; =\; \backslash dfrac\{\backslash text\{용질의\; 몰\; 수\}(\backslash mathrm\{mol\})\}\{\backslash text\{용액의\; 부피\}(\backslash mathrm\{L\})\}$이므로 몰 농도$(\mathrm{M})\times (\backslash mathrm\{M\})\backslash ,\backslash times\backslash ,$용액의 부피$(\mathrm{L})=(\backslash mathrm\{L\})\backslash ,=\backslash ,$용질의 몰 수$(\mathrm{m}\mathrm{o}\mathrm{l})(\backslash mathrm\{mol\})$이다.

따라서 $a\mathrm{M}\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(aq)1\mathrm{L}a\backslash ,\backslash mathrm\{M\}\backslash \; \backslash mathrm\{NaOH\}(aq)\backslash \; 1\backslash ,\backslash mathrm\{L\}$에는 $a\mathrm{M}\times 1\mathrm{L}=a\backslash ,\backslash mathrm\{M\}\; \backslash times\; 1\backslash ,\backslash mathrm\{L\}\; =\{\}$$a\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{L}\times 1\mathrm{L}=a\backslash ,\backslash mathrm\{mol/L\}\; \backslash times\; 1\backslash ,\backslash mathrm\{L\}\; =\{\}$$a\mathrm{m}\mathrm{o}\mathrm{l}a\backslash ,\backslash mathrm\{mol\}$의 $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\backslash mathrm\{NaOH\}$가,
$0.5\mathrm{M}\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(aq)2\mathrm{L}0.5\backslash ,\backslash mathrm\{M\}\backslash \; \backslash mathrm\{NaOH\}(aq)\backslash \; 2\backslash ,\backslash mathrm\{L\}$에는 $0.5\mathrm{M}\times 2\mathrm{L}=0.5\backslash ,\backslash mathrm\{M\}\; \backslash times\; 2\backslash ,\backslash mathrm\{L\}\; =\{\}$$0.5\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{L}\times 2\mathrm{L}=0.5\backslash ,\backslash mathrm\{mol/L\}\; \backslash times\; 2\backslash ,\backslash mathrm\{L\}\; =\{\}$$1\mathrm{m}\mathrm{o}\mathrm{l}1\backslash ,\backslash mathrm\{mol\}$의 $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\backslash mathrm\{NaOH\}$가,
$2\mathrm{M}\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}(aq)1\mathrm{L}2\backslash ,\backslash mathrm\{M\}\backslash \; \backslash mathrm\{NaOH\}(aq)\backslash \; 1\backslash ,\backslash mathrm\{L\}$에는 $2\mathrm{M}\times 1\mathrm{L}=2\backslash ,\backslash mathrm\{M\}\; \backslash times\; 1\backslash ,\backslash mathrm\{L\}\; =\{\}$$2\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{L}\times 1\mathrm{L}=2\backslash ,\backslash mathrm\{mol/L\}\; \backslash times\; 1\backslash ,\backslash mathrm\{L\}\; =\{\}$$2\mathrm{m}\mathrm{o}\mathrm{l}2\backslash ,\backslash mathrm\{mol\}$의 $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\backslash mathrm\{NaOH\}$가 포함되어 있음을 알 수 있다.

앞서 구한 내용을 바탕으로 각 용액에 포함되어 있는 $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\backslash mathrm\{NaOH\}$의 몰 수와 용액의 부피를 나타내면 아래 표와 같다.

ㄱ. (가)의 몰 농도는 $1\mathrm{M}1\backslash ,\backslash mathrm\{M\}$이므로
${\displaystyle \frac{(a+1)\mathrm{m}\mathrm{o}\mathrm{l}}{3\mathrm{L}}}=\backslash dfrac\{(a\; +\; 1)\backslash ,\backslash mathrm\{mol\}\}\{3\backslash ,\backslash mathrm\{L\}\}\; =\{\}$${\displaystyle \frac{a+1}{3}}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{L}=\backslash dfrac\{a\; +\; 1\}\{3\}\backslash ,\backslash mathrm\{mol/L\}\; =\{\}$$1\mathrm{M}1\backslash ,\backslash mathrm\{M\}$,
$a=2a\; =\; 2$이다. (O)

ㄴ. (가)에 녹아 있는 용질$(\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H})(\backslash mathrm\{NaOH\})$의 몰 수는 $(a+1)\mathrm{m}\mathrm{o}\mathrm{l}=3\mathrm{m}\mathrm{o}\mathrm{l}(a\; +\; 1)\backslash ,\backslash mathrm\{mol\}\; =\; 3\backslash ,\backslash mathrm\{mol\}$이며,
$\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\backslash mathrm\{NaOH\}$의 화학식량은 $4040$이므로 질량은 $3\mathrm{m}\mathrm{o}\mathrm{l}\times 40\mathrm{g}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}=120\mathrm{g}3\backslash ,\backslash mathrm\{mol\}\; \backslash times\; 40\backslash ,\backslash mathrm\{g/mol\}\; =\; 120\backslash ,\backslash mathrm\{g\}$이다. (X)

ㄷ. $a=2a\; =\; 2$이므로 (나)의 몰 농도는 ${\displaystyle \frac{(a+1+2)\mathrm{m}\mathrm{o}\mathrm{l}}{4\mathrm{L}}}=\backslash dfrac\{(a\; +\; 1\; +\; 2)\backslash ,\backslash mathrm\{mol\}\}\{4\backslash ,\backslash mathrm\{L\}\}\; =\{\}$${\displaystyle \frac{5}{4}}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{L}=\backslash dfrac\{5\}\{4\}\backslash ,\backslash mathrm\{mol/L\}\; =\{\}$${\displaystyle \frac{5}{4}}\mathrm{M}\backslash dfrac\{5\}\{4\}\backslash ,\backslash mathrm\{M\}$이다. (X)

따라서 답은 $11$번이다.