Answer:
MM = 58.41 g
Explanation:
First, the data we have is according to the hydrogen which is exerting pressure. To solve this, we need to use the ideal gas equation:
PV = nRT (1)
the molar mass of any compound is calculated like this:
MM = m/n (2)
So, from (1) we solve for the moles (n) and then, this value is replace in (2).
However, before we do all that, we need to gather all the correct data.
All the species in the reaction are solid or aqueous state, with the exception of hydrogen, which is gaseous. Hydrogen is collected over water, therefore, is exerting some pressure too. The problem is not indicating if the acid or any other species is exerting pressure, so we will assume that only hydrogen and water are exerting pressure.
The total pressure exerted by the system would be:
P = Pw + PH2 (3)
We already know the total pressure which is 756 torr.
This experiment is taking place at 25 °C (298.15 K), and at this temperature, we have a reported value for water pressure which is 23.8 Torr.
Let's solve for PH2:
PH2 = P - Pw
PH2 = 756 - 23 = 733 Torr
Now, with this value, and the volume and temperature, we can calculate the moles of H2:
n = PV/RT
But first, let's convert the pressure to atm:
PH2 = 733 Torr / 760 torr * 1 atm = 0.9644 atm
now, solving for n:
n = 0.9644 * (0.255) / 0.082 * 298.15
n = 0.0101 moles
Now that we have the moles, we know that the metal and the hydrogen has a mole ratio of 1:1 according to the reaction, so, this means that:
moles M = moles H2 = 0.0101 moles
We have the moles of the metal and the mass, we can calculate the molar mass using expression (2):
MM = 0.590/0.0101
MM = 58.41 g/mol
This is the molar mass of the metal
