calculate the work done when 50.0 g of tin dissolves in excess acid at 1.00 atm and 25c
Calculate the work done when 50.0g of tin dissolves in excess acid at 1.00 atm and 25 C
240 kj
1.04 kJ
To calculate the work done when tin dissolves in excess acid, we need to determine the change in volume and use the equation for work:
Work (W) = -P * ΔV
Where:
- Work (W) is the work done on or by the system,
- P is the pressure, and
- ΔV is the change in volume.
In this case, since the reaction is taking place at constant pressure (1.00 atm), the equation simplifies to:
Work (W) = -P * ΔV = -1.00 atm * ΔV
To find the change in volume (ΔV), we'll use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure,
- V is the volume,
- n is the number of moles of gas involved in the reaction,
- R is the ideal gas constant (0.0821 L·atm/(mol·K)), and
- T is the temperature in Kelvin.
First, we need to determine the number of moles of tin that will react. To do this, we'll use the molar mass of tin (Sn) and the given mass:
Molar mass of Sn = 118.71 g/mol
Number of moles of Sn = Mass of Sn / Molar mass of Sn
Given mass of Sn = 50.0 g
Number of moles of Sn = 50.0 g / 118.71 g/mol
Next, we need to convert the temperature from Celsius to Kelvin:
Temperature in Kelvin = 25°C + 273.15
Now we can calculate the work done:
Work (W) = -1.00 atm * ΔV
To find ΔV, we rearrange the ideal gas law equation:
ΔV = V final - V initial
Since the reaction takes place in solution, the initial volume can be assumed to be zero because the tin is solid. The final volume will be the volume of the gas produced by the reaction. Assuming complete reaction, the volume of the gas can be calculated using the ideal gas law:
V = nRT / P
Where:
- V is the volume of the gas,
- n is the number of moles of gas,
- R is the ideal gas constant, and
- P is the pressure.
Substituting the values into the equation, we can find the volume of the gas produced.
Once we have the volume of the gas, we can substitute it back into the equation for work done to calculate the final answer.