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Question 5.6: Graded Sodium bicarbonate (baking soda) is widely used to ab...

Graded

Sodium bicarbonate (baking soda) is widely used to absorb odors inside refrigerators. When acid is added to baking soda, the following reaction occurs:

NaHCO_{3}(s) + H^{+}(aq) → Na^{+}(aq) + CO_{2}(g) + H_{2}O

All experiments here are performed with 2.45 M HCl and 12.75 g of NaHCO_{3} at 732 mm Hg and 38°C.

ⓐ If an excess of HCl is used, what volume of CO_{2} is obtained?
ⓑ If NaHCO_{3} is in excess, what volume of HCl is required to produce 2.65 L of CO_{2}?
ⓒ What volume of CO_{2} is produced when all the NaHCO_{3} is made to react with 50.0 mL of HCl?

ANALYSIS
pressure (732 mm Hg); temperature (38°C); mass of NaHCO_{3} (12.75 g) Information given:
molar mass of NaHCO_{3}
stoichiometric ratio: 1 NaHCO_{3} /1 CO_{2}
Information implied:
volume of CO_{2} produced Asked for:

STRATEGY

1. Follow the flow chart in Figure 5.5.
2. Convert to appropriate units of pressure and temperature.

mass_{NaHCO_{3}}  \underrightarrow{MM}  n_{NaHCO_{3}} \overset{stoichiometric}{\underset{ratio}{\longrightarrow }}  n_{CO_{2}}  \underrightarrow{PV  =  nRT}V_{CO_{2}}

ANALYSIS
pressure (732 mm Hg); temperature (38°C);
volume of CO_{2} produced (2.65 L);
molarity of HCl (2.45 M)
Information given:
H^{+} is the reacting species. HCl is the parent compound.
stoichiometric ratio: 1 H^{+}/1 CO_{2}
Information implied:

STRATEGY

Follow the flowchart in Figure 5.5.

V_{CO_{2}}  \underrightarrow{PV  =  nRT}  n_{CO_{2}}  \overset{stoichiometric}{\underset{ratio}{\longrightarrow }}  n_{H^{+}}  \overset{atom}{\underset{ratio}{\longrightarrow }}  n_{HCl}  \underrightarrow{M}  V_{HCl}

ANALYSIS
molarity of HCl (2.45 M); volume of HCl (50.0 mL);
pressure (732 mm Hg); temperature (38°C)
Information given:
H^{+} is the reacting species. HCl is the parent compound.
stoichiometric ratios: 1 H^{+}/1 CO_{2}; 1 NaHCO_{3} /1 CO_{2}
from part (a): mol NaHCO_{3}
Information implied:

STRATEGY

1. The presence of enough given data to calculate the number of moles of each reactant tells you that part (c) is a limiting reactant problem.
2. Follow the flow chart in Figure 5.5 to determine the number of moles of CO_{2} obtained if HCl is limiting. You can obtain the moles of CO_{2} if NaHCO_{3} is limiting from part (a).
3. Compare the moles of CO_{2} obtained using H^{+} as the limiting reactant to the moles of CO_{2} obtained using NaHCO_{3} as the limiting reactant. Choose the smaller number of moles of CO_{2}.
4. Use the ideal gas law to convert mol CO_{2} to the volume of CO_{2}.

fig 5.5
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