6. What mass of sodium carbonate must be used to produce 10.36 L of carbon dioxide at \( 24^{\circ} \mathrm{C} \) and 103 kPa according to the following neutralization reaction? \[ \mathrm{HCl}_{(\mathrm{aq})}+\mathrm{Na}_{2} \mathrm{CO}_{3(\mathrm{~s})} \rightarrow \mathrm{NaCl}_{(\mathrm{aq})}+\mathrm{CO}_{2(\mathrm{~g})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})} \]
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Beyond the Answer
To determine the mass of sodium carbonate (\( \mathrm{Na}_2\mathrm{CO}_3 \)) required to produce 10.36 L of \( \mathrm{CO}_2 \) at \( 24^{\circ} \mathrm{C} \) and 103 kPa, we can start with the ideal gas law. The ideal gas law is given by: \[ PV = nRT \] First, we need to use the ideal gas constant \( R = 8.314 \, \mathrm{J/(mol \cdot K)} \) or \( 0.08314 \, \mathrm{L \cdot kPa/(mol \cdot K)} \) depending on the units. To convert the temperature to Kelvin: \[ T = 24 + 273.15 = 297.15 \, K \] Now, rearranging the ideal gas equation for \( n \) (the number of moles of \( \mathrm{CO}_2 \)): \[ n = \frac{PV}{RT} = \frac{(103 \, \text{kPa})(10.36 \, \text{L})}{(0.08314 \, \text{L} \cdot \text{kPa/(mol \cdot K)})(297.15 \, K)} \] Calculating \( n \): \[ n \approx \frac{1060.48}{24.77} \approx 42.75 \, \text{mol of } \mathrm{CO}_2 \] From the reaction, we see that 1 mole of \( \mathrm{Na}_2\mathrm{CO}_3 \) produces 1 mole of \( \mathrm{CO}_2 \). Therefore, we need 42.75 moles of \( \mathrm{Na}_2\mathrm{CO}_3 \). The molar mass of \( \mathrm{Na}_2\mathrm{CO}_3 \) is approximately: \[ 2(22.99) + 12.01 + 3(16.00) = 105.99 \, \mathrm{g/mol} \] Finally, we can find the mass needed: \[ \text{mass} = n \times \text{molar mass} = 42.75 \, \text{mol} \times 105.99 \, \text{g/mol} \approx 4525 \, \text{grams} \] So, you would need approximately 4525 grams of sodium carbonate to produce 10.36 L of carbon dioxide under the specified conditions!
