750 ml of nitrogen are collected over water at 25•c and 740mm pressure of the aqueous tension at this temperatures is 23.8 mm hg. calculate the mass of dry gas
Give answer
To calculate the mass of dry gas, we need to consider the vapor pressure of water at the given temperature and subtract it from the total pressure. Here are the step-by-step calculations:
Step 1: Convert the pressure of the aqueous tension to atm.
The pressure of the aqueous tension is given as 23.8 mmHg. We need to convert it to atm by dividing it by 760 mmHg (since 1 atm = 760 mmHg).
23.8 mmHg / 760 mmHg = 0.0313 atm
Step 2: Calculate the partial pressure of the nitrogen gas.
The partial pressure of the nitrogen gas (P[N2]) is obtained by subtracting the pressure of the aqueous tension from the total pressure.
Partial pressure of nitrogen gas (P[N2]) = Total pressure (Ptotal) - Pressure of the aqueous tension (P[H2O])
P[N2] = 740 mmHg - 23.8 mmHg
Step 3: Convert the partial pressure of nitrogen gas to atm.
Convert the partial pressure of nitrogen gas from mmHg to atm by dividing it by 760 mmHg.
P[N2] (atm) = (740 mmHg - 23.8 mmHg) / 760 mmHg
Step 4: Convert the volume of nitrogen gas to liters.
The volume of nitrogen gas is given as 750 ml. We need to convert it to liters by dividing it by 1000.
Volume of nitrogen gas (V) in liters = 750 ml / 1000 ml/L
Step 5: Calculate the mass of dry gas using the ideal gas law.
The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
Rearranging the equation to solve for mass (m), we get m = (P * V) / (R * T).
Step 6: Calculate the mass of dry gas.
mass (m) = (P[N2] * V) / (R * T)
Now we need the value for R, the universal gas constant, which is 0.0821 L atm/(K mol). And we need the value for T, the temperature, which is 25°C or 298 K.
Step 7: Plug in the values and calculate the mass of dry gas.
mass (m) = (P[N2] * V) / (R * T)
mass (m) = (P[N2] (atm) * V (L)) / (R (L atm/(K mol)) * T (K))
To calculate the mass of dry gas in this scenario, we need to consider the partial pressure of nitrogen and its relationship to the total pressure.
1. First, let's calculate the partial pressure of nitrogen. We can use Dalton's law of partial pressures, which states that the total pressure is the sum of the partial pressures of each component in a mixture. In this case, the total pressure is 740 mmHg, and the aqueous tension is 23.8 mmHg. Therefore, the partial pressure of nitrogen can be calculated as follows:
Partial pressure of nitrogen = Total pressure - Aqueous tension
Partial pressure of nitrogen = 740 mmHg - 23.8 mmHg = 716.2 mmHg
2. Now that we have the partial pressure, we can use the ideal gas law to find the number of moles of nitrogen. The ideal gas law equation is:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
First, we need to convert the volume from milliliters (ml) to liters (L). Since 1 liter = 1000 ml, 750 ml is equal to 0.75 L.
Next, we need to convert the temperature from Celsius (°C) to Kelvin (K). The conversion is done by adding 273.15 to the Celsius temperature. So, 25°C + 273.15 = 298.15 K.
Now we can rearrange the ideal gas law equation to solve for the number of moles:
n = (PV) / (RT)
n = (716.2 mmHg * 0.75 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
3. Solve the equation to determine the number of moles of nitrogen:
n = (716.2 mmHg * 0.75 L) / (0.0821 L·atm/(mol·K) * 298.15 K) ≈ 27.27 mol
4. Finally, we can calculate the mass of the dry gas using the molar mass of nitrogen, which is about 28.0134 g/mol:
Mass of dry gas = Number of moles * Molar mass
Mass of dry gas = 27.27 mol * 28.0134 g/mol ≈ 764.04 g
Therefore, the mass of dry gas collected is approximately 764.04 grams.