A sample of iron reacted with hydrochloric acid. The liberated hydrogen occupied 40.1 mL when collected over water at 27 C at a barometric pressure of 750 torr. What is the mass of the sample of iron? (Because of the collection of gas over water, the vapor pressure of the water must be subtracted from the barometric pressure to find the pressure of the hydrogen gas.)
Fe(s)+ 2HCl(aq)=FeCl2(aq)+ H2(g)
To find the mass of the sample of iron, we need to use the Ideal Gas Law and perform some calculations.
First, we need to calculate the pressure of the hydrogen gas by subtracting the vapor pressure of water from the barometric pressure. The vapor pressure of water at 27°C is typically around 26.7 torr. So, the pressure of the hydrogen gas is 750 torr - 26.7 torr = 723.3 torr.
Next, we need to convert the volume of hydrogen gas from milliliters (mL) to liters (L). There are 1000 mL in 1 L, so the volume of hydrogen gas is 40.1 mL / 1000 = 0.0401 L.
Now, we can use the Ideal Gas Law equation PV = nRT to find the number of moles of hydrogen gas. P is the pressure in atmospheres (atm), V is the volume in liters (L), 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 (K).
We need to convert the pressure of the hydrogen gas from torr to atm by dividing by 760 (since 1 atm = 760 torr) and convert the temperature from Celsius to Kelvin by adding 273.15.
So, the equation becomes: (723.3 torr / 760 torr/atm) * (0.0401 L) = n * (0.0821 L·atm/(mol·K)) * (27°C + 273.15)
Simplifying, we get: 0.03927 = n * 0.0821 * 300.15
Solving for n (the number of moles of hydrogen gas), we find: n ≈ 0.001586 moles
According to the balanced chemical equation, the mole ratio between iron and hydrogen gas is 1:1. This means that for every 1 mole of iron reacted, 1 mole of hydrogen gas is produced.
So, the number of moles of iron reacted is also approximately 0.001586 moles.
The molar mass of iron (Fe) is 55.845 grams/mole.
Therefore, the mass of the sample of iron is: mass = number of moles * molar mass = 0.001586 moles * 55.845 grams/mole = 0.0889 grams.
Hence, the mass of the sample of iron is approximately 0.0889 grams.