Sometimes in lab we collect the gas formed by a chemical reaction over water (see sketch at right). This makes it easy to isolate and measure the amount of gas produced.Suppose the H2 gas evolved by a certain chemical reaction taking place at 30.0°C is collected over water, using an apparatus something like that in the sketch, and the final volume of gas in the collection tube is measured to be 40.0mL.Sketch of a gas-collection apparatusCalculate the mass of H2 that is in the collection tube. Round your answer to 2 significant digits. You can make any normal and reasonable assumption about the reaction conditions and the nature of the gases.
Question
Sometimes in lab we collect the gas formed by a chemical reaction over water (see sketch at right). This makes it easy to isolate and measure the amount of gas produced.Suppose the H2 gas evolved by a certain chemical reaction taking place at 30.0°C is collected over water, using an apparatus something like that in the sketch, and the final volume of gas in the collection tube is measured to be 40.0mL.Sketch of a gas-collection apparatusCalculate the mass of H2 that is in the collection tube. Round your answer to 2 significant digits. You can make any normal and reasonable assumption about the reaction conditions and the nature of the gases.
Solution
To calculate the mass of H2 gas, we need to use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15. So, 30.0°C = 303.15 K.
Next, we need to find the pressure of the H2 gas. The problem doesn't give us the pressure directly, but we can assume that the pressure of the gas is equal to the atmospheric pressure because the gas is collected over water. The standard atmospheric pressure at sea level is 1 atm.
The volume of the gas is given as 40.0 mL. We need to convert this to liters because the ideal gas constant R is usually given in terms of L·atm/mol·K. So, 40.0 mL = 0.040 L.
Now we can plug these values into the ideal gas law equation to find the number of moles of H2 gas:
(1 atm)(0.040 L) = n(0.0821 L·atm/mol·K)(303.15 K)
Solving for n gives n = 0.00163 moles of H2.
Finally, we can find the mass of the H2 gas by multiplying the number of moles by the molar mass of H2. The molar mass of H2 is approximately 2.02 g/mol, so the mass of the H2 gas is (0.00163 moles)(2.02 g/mol) = 0.0033 g.
So, the mass of H2 in the collection tube is approximately 0.0033 g, or 3.3 mg when rounded to two significant digits.
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