Answer :
The mass of the magnesium ribbon used is 0.0382 grams.
To find the mass of the magnesium ribbon used, we need to go through several steps:
Convert atmospheric pressure:
- 29.18 inches Hg to torr.
- Using the conversion factor, 1 inch Hg = 25.4 torr, the atmospheric pressure is 29.18 inches Hg × 25.4 = 741.17 torr.
- Correct for water vapor pressure:
- At 22.4°C, the vapor pressure of water is approximately 21.07 torr.
- The total pressure of the hydrogen gas collected over water is then 741.17 torr - 21.07 torr = 720.10 torr.
Correct for the height difference:
- The height difference of 18.4 cm of water should be converted to pressure.
- Since 1 cm H₂O = 0.7356 torr,
- 18.4 cm H₂O = 18.4 × 0.7356 = 13.53 torr.
- Therefore, the pressure of hydrogen gas is 720.10 torr - 13.53 torr = 706.57 torr.
Use the Ideal Gas Law: PV = nRT.
- With the corrected pressure, volume, and temperature, calculate the moles of hydrogen gas (H₂).
- Convert 37.1 mL to liters:
- 37.1 mL = 0.0371 L.
- Using R = 0.0821 L·atm·K⁻¹·mol⁻¹ (and converting pressure in torr to atm, 1 atm = 760 torr), we get,
- P = 706.57 torr / 760 = 0.929 atm.
- Temperature in Kelvin: 22.4°C + 273.15 = 295.55 K.
Solving for n,
- n = (P×V) / (R×T):
- [tex]n &= \frac{(0.929 \, \text{atm} \times 0.0371 \, \text{L})}{(0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \times 295.55 \, \text{K})} \\ \\n &= \frac{0.03446}{24.259} \\ \\n &= 0.00142 \, \text{moles of H}_2[/tex]
Relate moles of H₂ to moles of Mg:
Since the reaction between Mg and HCl produces hydrogen gas by Mg + 2HCl → MgCl₂ + H₂, 1 mole of Mg produces 1 mole of H₂.
Therefore, moles of Mg = moles of H₂ = 0.00157 moles.
Calculate mass of Mg:
Using the molar mass of Mg (24.305 g/mol),
mass = moles × molar mass = 0.00157 moles × 24.305 g/mol = 0.0382 g.
Final answer:
To calculate the mass of the magnesium ribbon used in the experiment, we need more information, such as the length or width of the ribbon or the density of the magnesium ribbon. Without this additional information, we cannot determine the mass of the ribbon.
Explanation:
To calculate the mass of the magnesium ribbon used, we need to consider the reaction between magnesium and hydrochloric acid (assuming this is the experiment being conducted). The balanced chemical equation for this reaction is:
Mg + 2HCl → MgCl2 + H2
From the balanced equation, we know that the molar ratio between magnesium and hydrogen gas is 1:1. This means that for every 1 mole of magnesium reacted, 1 mole of hydrogen gas is produced.
To find the moles of hydrogen gas produced, we can use the Ideal Gas Law:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas (in K)
We know the volume of hydrogen gas collected (37.1 mL) and the temperature (22.4 degrees Celsius, which is 295.55 K). However, we need to convert the pressure from inches Hg to atm.
1 atm = 29.92 inches Hg
First, let's convert the pressure to atm:
29.18 inches Hg * (1 atm / 29.92 inches Hg) = 0.973 atm
Next, let's convert the volume from mL to L:
37.1 mL * (1 L / 1000 mL) = 0.0371 L
Now, we can plug in the values into the Ideal Gas Law equation:
(0.973 atm) * (0.0371 L) = n * (0.0821 L·atm/mol·K) * (295.55 K)
Solving for n, we find:
n = (0.973 * 0.0371) / (0.0821 * 295.55)
n = 0.00127 moles
Since the molar ratio is 1:1 between magnesium and hydrogen gas, this means that 0.00127 moles of magnesium reacted.
Now we can calculate the molar mass of magnesium:
Molar mass of magnesium (Mg) = mass / moles
Molar mass of magnesium (Mg) = mass (grams) / 0.00127 moles
Given that the volume of the hydrogen gas collected was 37.1 mL and the difference in water level between the beaker and the burette is 18.4 cm, we need to find the mass of the magnesium ribbon. Unfortunately, the information provided does not provide enough information to directly find the mass of the magnesium ribbon. Additional information is needed, such as the length or width of the ribbon, or the density of the magnesium ribbon, in order to calculate its mass.
Therefore, without more information, we cannot determine the mass of the magnesium ribbon used.
