Calculate the work done when 70.0 g of tin are dissolved in excess acid at 1.00 atm and 29°C. Assume ideal gas behavior.
Sn(s) + 2 H+(aq) Sn2+(aq) + H2(g)
what???
The given chemical equation represents the reaction of tin (Sn) with acid. In this reaction, tin reacts with hydrogen ions (H+) to produce tin ions (Sn2+) and hydrogen gas (H2). The question asks us to calculate the work done during this reaction.
To calculate the work done, we need to determine the change in volume of the system. In this case, the only change in volume occurs due to the production of hydrogen gas. The ideal gas law equation, PV = nRT, can be used to calculate the change in volume.
First, we need to calculate the moles of hydrogen gas produced. According to the balanced chemical equation, 1 mole of tin reacts to produce 1 mole of hydrogen gas. So, the moles of hydrogen gas can be calculated by dividing the mass of tin (given as 70.0 g) by the molar mass of tin.
The molar mass of tin (Sn) is 118.71 g/mol. Therefore, the moles of tin (Sn) can be calculated as:
moles of Sn = mass of Sn / molar mass of Sn
moles of Sn = 70.0 g / 118.71 g/mol = 0.589 mol
Since the stoichiometric ratio between tin and hydrogen gas is 1:1, the moles of hydrogen gas produced is also 0.589 mol.
Now, we can use the ideal gas law to calculate the change in volume:
PV = nRT
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = 29°C + 273.15 = 302.15 K
The pressure is given as 1.00 atm.
R is the ideal gas constant, which is 0.0821 L•atm/(mol•K).
Substituting the values into the ideal gas law equation, we have:
(1.00 atm)V = (0.589 mol)(0.0821 L•atm/(mol•K))(302.15 K)
Simplifying the equation:
V = (0.589 mol)(0.0821 L•atm/(mol•K))(302.15 K) / 1.00 atm
V ≈ 14.69 L
The change in volume is approximately equal to 14.69 liters.
Finally, we can calculate the work done using the equation:
Work = -PΔV
Plugging in the values:
Work = -(1.00 atm)(14.69 L) = -14.69 L•atm
Therefore, the work done when 70.0 g of tin are dissolved in excess acid under the given conditions is approximately -14.69 L•atm. The negative sign indicates that work is done on the system, meaning energy is absorbed from the surroundings.