A method of removing CO₂ from a spacecraft is to allow the CO₂ to react with sodium hydroxide. (The products of the reaction are sodium carbonate and water.) What volume of carbon dioxide at 25^$\circ$C and 749 mmHg can be removed per kilogram of sodium hydroxide that reacts A) 276 L B) 284 L C) 301 L D) 310 L E) 620 L

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The first step is to write the balanced chemical equation for the reaction between CO₂ and sodium hydroxide: CO₂ + 2 NaOH → Na2CO3 + H2O From this equation, we can see that one mole of CO₂ reacts with two moles of NaOH to produce one mole of CO2. Therefore, we need to know how many moles of NaOH are present in one kilogram of NaOH. The molar mass of NaOH is 40.00 g/mol, so one kilogram contains 25 mol: 1 kg NaOH × (1000 g/kg) / (40.00 g/mol) = 25 mol NaOH Since two moles of NaOH react with one mole of CO₂ to produce one mole of CO2, we can remove 12.5 mol of CO₂ with one kilogram of NaOH. Using the ideal gas law, we can calculate the volume of CO2 produced: PV = nRT V = nRT/P V = (12.5 mol)(0.0821 L·atm/mol·K)(298 K)/(749 mmHg × 101.3 kPa/1 atm) V = 310 L Therefore, the answer is D, 310 L of CO2 can be removed per kilogram of NaOH that reacts.

A Method of Removing CO2 from a Spacecraft Is to Allow

A Method of Removing CO₂ from a Spacecraft Is to Allow