Question

In order to determine the rate of photosynthesis (the conversion by plants of carbon dioxide and water into glucose and oxygen), the oxygen gas emitted by an aquatic plant is collected over water at a temperature of 293 K and a total pressure of 754.0 mmHg. Over a specific time-period, a total of 1.62 L of gas is collected. The partial pressure of water at 293 K is 17.55 mmHg. What mass of oxygen gas (in grams) forms

Answer 1

The mass of oxygen gas collected is calculated by using the ideal gas law to find the number of moles of oxygen and then multiplying by the molar mass of oxygen, resulting in approximately 2.17 grams of O2.

Step-by-step explanation:

To calculate the mass of oxygen gas collected from photosynthesis, first, the partial pressure of oxygen must be found by subtracting the water vapor pressure from the total pressure. The partial pressure of oxygen is then used with the ideal gas law to find the number of moles of oxygen.

Given the total pressure is 754.0 mmHg and the partial pressure of water at 293 K is 17.55 mmHg, the partial pressure of oxygen (O₂) is:

Partial pressure of O₂ = Total pressure - Vapor pressure of water
= 754.0 mmHg - 17.55 mmHg
= 736.45 mmHg

To convert the pressure to atmospheres (a unit more convenient for use in the ideal gas law), we use the conversion factor 1 atm = 760 mmHg:

Pressure of O₂ (in atm) = 736.45 mmHg / 760 mmHg/atm
≈ 0.9695 atm

Now, using the ideal gas law PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant (0.0821 L atm/mol K), and T is the temperature in Kelvin:

n = PV / RT
≈ (0.9695 atm) × (1.62 L) / (0.0821 L atm/mol K * 293 K)
≈ 0.0679 moles of O₂

The molar mass of O₂ is approximately 32.00 g/mol, so:

Mass of O₂ = n ×molar mass
= 0.0679 moles×32.00 g/mol
≈ 2.17 grams of O₂

Answer 2

2.87 g

Step-by-step explanation:

Step 1: Given data

• Temperature (T): 293 K

• Total pressure (P): 754.0 mmHg

• Partial pressure of water (pW): 17.55 mmHg

• Volume of gas (V): 1.62 L

Step 2: Calculate the partial pressure of CO₂

The total pressure is the sum of the partial pressures of CO₂and water.

P = pCO₂ + pW

pCO₂ = P - pW = 754.0 mmHg - 17.55 mmHg = 736.5 mmHg

We will convert this pressure to atm using the conversion factor 1 atm = 760 mmHg.

736.5 mmHg × 1 atm/760 mmHg = 0.9691 atm

Step 3: Calculate the moles (n) of CO₂

We will use the ideal gas equation.

P × V = n × R × T

n = P × V/R × T

n = 0.9691 atm × 1.62 L/(0.0821 atm.L/mol.K) × 293 K = 0.0653 mol

Step 4: Calculate the mass corresponding to 0.0653 moles of CO₂

The molar mass of CO₂ is 44.01 g/mol.

0.0653 mol × 44.01 g/mol = 2.87 g