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In a balloon of total pressure 6 atm there is a gaseous composition of 44 grams of carbon dioxide 16 grams of by oxygen and 7 grams of nitrogen, what is the ratio of nitrogen partial pressure do the total pressure in the balloon?
- a)0.25
- b)0.5
- c)0.75
- d)1
Correct answer is option 'A'. Can you explain this answer?
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In a balloon of total pressure 6 atm there is a gaseous composition of...
To find the ratio of nitrogen partial pressure to the total pressure in the balloon, we need to calculate the partial pressure of nitrogen and divide it by the total pressure.
First, we need to calculate the number of moles of each gas present in the balloon:
- Moles of carbon dioxide (CO2) = mass of CO2 / molar mass of CO2
= 44 g / 44 g/mol
= 1 mole of CO2
- Moles of oxygen (O2) = mass of O2 / molar mass of O2
= 16 g / 32 g/mol
= 0.5 moles of O2
- Moles of nitrogen (N2) = mass of N2 / molar mass of N2
= 7 g / 28 g/mol
= 0.25 moles of N2
Next, we need to calculate the partial pressure of each gas using the ideal gas law equation:
PV = nRT
- For carbon dioxide:
Partial pressure of CO2 = (moles of CO2 * gas constant * temperature) / volume
= (1 mole * 0.0821 atm/mol·K * T) / V
- For oxygen:
Partial pressure of O2 = (moles of O2 * gas constant * temperature) / volume
= (0.5 moles * 0.0821 atm/mol·K * T) / V
- For nitrogen:
Partial pressure of N2 = (moles of N2 * gas constant * temperature) / volume
= (0.25 moles * 0.0821 atm/mol·K * T) / V
Since we are looking for the ratio of nitrogen partial pressure to the total pressure, we can write:
Ratio = Partial pressure of N2 / Total pressure
The total pressure is given as 6 atm. Therefore, the ratio of nitrogen partial pressure to the total pressure is:
Ratio = [(0.25 moles * 0.0821 atm/mol·K * T) / V] / 6 atm
Simplifying, we can cancel out the units and rearrange the equation:
Ratio = (0.25 * 0.0821 * T) / (6 * V)
Since the question only asks for the ratio, the specific values of temperature and volume are not necessary for the calculation. So, we can conclude that the ratio of nitrogen partial pressure to the total pressure in the balloon is 0.25, which corresponds to option A.
First, we need to calculate the number of moles of each gas present in the balloon:
- Moles of carbon dioxide (CO2) = mass of CO2 / molar mass of CO2
= 44 g / 44 g/mol
= 1 mole of CO2
- Moles of oxygen (O2) = mass of O2 / molar mass of O2
= 16 g / 32 g/mol
= 0.5 moles of O2
- Moles of nitrogen (N2) = mass of N2 / molar mass of N2
= 7 g / 28 g/mol
= 0.25 moles of N2
Next, we need to calculate the partial pressure of each gas using the ideal gas law equation:
PV = nRT
- For carbon dioxide:
Partial pressure of CO2 = (moles of CO2 * gas constant * temperature) / volume
= (1 mole * 0.0821 atm/mol·K * T) / V
- For oxygen:
Partial pressure of O2 = (moles of O2 * gas constant * temperature) / volume
= (0.5 moles * 0.0821 atm/mol·K * T) / V
- For nitrogen:
Partial pressure of N2 = (moles of N2 * gas constant * temperature) / volume
= (0.25 moles * 0.0821 atm/mol·K * T) / V
Since we are looking for the ratio of nitrogen partial pressure to the total pressure, we can write:
Ratio = Partial pressure of N2 / Total pressure
The total pressure is given as 6 atm. Therefore, the ratio of nitrogen partial pressure to the total pressure is:
Ratio = [(0.25 moles * 0.0821 atm/mol·K * T) / V] / 6 atm
Simplifying, we can cancel out the units and rearrange the equation:
Ratio = (0.25 * 0.0821 * T) / (6 * V)
Since the question only asks for the ratio, the specific values of temperature and volume are not necessary for the calculation. So, we can conclude that the ratio of nitrogen partial pressure to the total pressure in the balloon is 0.25, which corresponds to option A.
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In a balloon of total pressure 6 atm there is a gaseous composition of...
The partial pressure of a gas is given by the mole fraction of the gas x the total pressure, so the ratio of the partial pressure to the total pressure is the mole fraction of nitrogen is 7/14 divided by 44/44 + 16/32 2 + 7/14 = 0.25.
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