29. the $delta h$ for the solution process when solid sodium hydroxide dissolves in water is -44.4…

29. the $delta h$ for the solution process when solid sodium hydroxide dissolves in water is -44.4 $\frac{kj}{mol naoh}$. when a 13.9 - g sample of naoh dissolves in 250.0 g of water in a coffee - cup calorimeter, calculate the change in temperature. assume that the solution has the same specific heat capacity as liquid water, 4.18 $\frac{j}{g^{circ}c}$. the molar mass of naoh is 40 $\frac{g}{mol}$. the mass of the solution is the sum of the mass of the solute and the solvent.\n\na. - 9.0$^{circ}c$\nb. 9.0$^{circ}c$\nc. - 14.0$^{circ}c$\nd. 14.0$^{circ}c$

29. the $delta h$ for the solution process when solid sodium hydroxide dissolves in water is -44.4 $\frac{kj}{mol naoh}$. when a 13.9 - g sample of naoh dissolves in 250.0 g of water in a coffee - cup calorimeter, calculate the change in temperature. assume that the solution has the same specific heat capacity as liquid water, 4.18 $\frac{j}{g^{circ}c}$. the molar mass of naoh is 40 $\frac{g}{mol}$. the mass of the solution is the sum of the mass of the solute and the solvent.\n\na. - 9.0$^{circ}c$\nb. 9.0$^{circ}c$\nc. - 14.0$^{circ}c$\nd. 14.0$^{circ}c$

Answer

Explanation:

Step1: Calculate moles of NaOH

$n=\frac{m}{M}=\frac{13.9\ g}{40\ g/mol}=0.3475\ mol$

Step2: Calculate heat released

$q = n\times\Delta H=0.3475\ mol\times44.4\ kJ/mol = 0.3475\times44.4\times1000\ J=15429\ J$

Step3: Calculate mass of solution

$m_{solution}=13.9\ g + 250.0\ g=263.9\ g$

Step4: Use heat - capacity formula to find $\Delta T$

$q = mc\Delta T$, so $\Delta T=\frac{q}{mc}=\frac{15429\ J}{263.9\ g\times4.18\ J/(g\cdot^{\circ}C)}\approx14.0^{\circ}C$

Answer:

D. $14.0^{\circ}C$