Assume that 5.00 grams of zinc react with excess HCl according to the following equation:
Zn + 2HCl = ZnCl2 + H2
The hydrogen was collected over water at 20.0C and the prssure of the atmosphere is 751 mmHg. The pressure of the water vapor at 20C is 17.5 mmHg. How many moles of hydrogen gas should be produced? Determine the theoretical volume in liters of the H2 collected.
moles H2=molesZn=5/30=1/6
PV=nRT
V=nR(273+20)/(751-17.5)
n is 1/6, R is in units of liters*mmHg/K
verify you have the correct gas constant in those units.
To determine the number of moles of hydrogen gas produced and the corresponding volume in liters, 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 gas constant, and T is the temperature in Kelvin.
1. First, let's determine the pressure of the hydrogen gas. The pressure inside the collection vessel is equal to the atmospheric pressure minus the pressure of the water vapor. Therefore, P = Patm - Pwater.
In this case, the atmospheric pressure (Patm) is 751 mmHg, and the pressure of water vapor (Pwater) is 17.5 mmHg. So, the pressure of the hydrogen gas is 751 mmHg - 17.5 mmHg = 733.5 mmHg.
2. Next, convert the pressure from mmHg to atm by dividing it by 760 mmHg/atm. Thus, the pressure becomes 733.5 mmHg / 760 mmHg/atm = 0.964 atm.
3. Convert the temperature from Celsius to Kelvin by adding 273.15. In this case, 20.0°C + 273.15 = 293.15 K.
4. The volume of the collected hydrogen gas can be determined by rearranging the ideal gas law equation: V = (nRT) / P.
However, we need to solve for n first. To do this, we can use stoichiometry and the balanced chemical equation provided.
The balanced equation tells us that 1 mole of zinc (Zn) reacts to produce 1 mole of hydrogen gas (H2). Therefore, the number of moles of hydrogen gas produced will be equal to the number of moles of zinc used in the reaction.
To determine the number of moles of zinc used, we need to use its molar mass. The molar mass of zinc (Zn) is 65.38 g/mol.
Therefore, the number of moles of zinc used in the reaction is given by: moles of Zn = mass of Zn / molar mass of Zn.
In this case, the mass of Zn used is 5.00 g, so moles of Zn = 5.00 g / 65.38 g/mol = 0.0764 mol.
Now we have the number of moles of hydrogen gas (n = 0.0764 mol), the gas constant (R = 0.0821 L·atm/mol·K), the temperature (T = 293.15 K), and the pressure (P = 0.964 atm). Let's substitute these values into the rearranged ideal gas law equation:
V = (0.0764 mol * 0.0821 L·atm/mol·K * 293.15 K) / 0.964 atm
V ≈ 1.91 L
Therefore, the theoretical volume of hydrogen gas collected is approximately 1.91 liters.