When carbon dioxide dissolves in water, it sometimes reacts with water to form carbonic acid as in this balanced equation:
[tex]CO_2+H_2 O \rightarrow H_2 CO_3[/tex].
If 495 milliliters of carbon dioxide at [tex]25^{\circ} C[/tex] and 101.3 kilopascals reacts with excess water, what is the theoretical yield of carbonic acid?
Use the periodic table and the ideal gas resource.
A. 0.889 g
B. 1.10 g
C. 1.27 g
D. 2.02 g
Answer (2)
The theoretical yield of carbonic acid when 495 mL of carbon dioxide reacts with excess water is approximately 1.25 g. Therefore, the closest answer choice is C. 1.27 g.
;
Convert the volume of C O 2 to liters: V = 0.495 L .
Convert the temperature to Kelvin: T = 298.15 K .
Use the ideal gas law to find moles of C O 2 : n ≈ 0.0202 m o l .
Calculate the mass of H 2 C O 3 : mass ≈ 1.25 g . The closest answer is 1.27 g .
Explanation
Problem Analysis We are given the volume, pressure, and temperature of carbon dioxide ( C O 2 ) and asked to find the theoretical yield of carbonic acid ( H 2 C O 3 ) when C O 2 reacts with excess water according to the balanced equation:
C O 2 + H 2 O → H 2 C O 3
We will use the ideal gas law to find the number of moles of C O 2 , and then use the stoichiometry of the reaction to find the theoretical yield of H 2 C O 3 .
Convert Volume First, convert the volume of C O 2 from milliliters (mL) to liters (L):
V C O 2 = 495 mL = 0.495 L
Convert Temperature Next, convert the temperature from Celsius ( ∘ C ) to Kelvin (K):
T = 2 5 ∘ C + 273.15 = 298.15 K
Calculate Moles of CO2 Now, use the ideal gas law to find the number of moles ( n ) of C O 2 :
P V = n RT
Where:
P = 101.3 kPa (pressure) V = 0.495 L (volume) R = 8.314 mol K L kPa (ideal gas constant) T = 298.15 K (temperature)
Solve for n :
n = RT P V = ( 8.314 mol K L kPa ) ( 298.15 K ) ( 101.3 kPa ) ( 0.495 L ) ≈ 0.0202 mol
Moles of H2CO3 Since the mole ratio of C O 2 to H 2 C O 3 is 1:1, the number of moles of H 2 C O 3 is equal to the number of moles of C O 2 :
n H 2 C O 3 = n C O 2 ≈ 0.0202 mol
Molar Mass of H2CO3 Calculate the molar mass of H 2 C O 3 :
M H 2 C O 3 = 2 ( 1.008 ) + 12.01 + 3 ( 16.00 ) = 62.026 g/mol
(Using the molar masses from the periodic table: H = 1.008, C = 12.01, O = 16.00)
Theoretical Yield Calculate the theoretical yield of H 2 C O 3 in grams:
mass = n H 2 C O 3 × M H 2 C O 3 ≈ 0.0202 mol × 62.026 g/mol ≈ 1.25 g
Final Answer The theoretical yield of carbonic acid is approximately 1.25 g. Therefore, the closest answer choice is C. 1.27 g.
Examples
Understanding the reaction between carbon dioxide and water to form carbonic acid is crucial in environmental science. For instance, it helps in predicting ocean acidification due to increased atmospheric CO2 levels. By calculating the theoretical yield, scientists can estimate how much carbonic acid will form under specific conditions, aiding in the development of strategies to mitigate the impact of climate change on marine ecosystems. This calculation is also relevant in industrial processes where CO2 is captured and converted into valuable products.
