Question

A mixture of hydrogen and oxygen has volume 2000 cm³, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:

[Take gas constant R=8.3JK⁻¹mol⁻¹]

Answer 1

To find the ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture, we can use the ideal gas law. Given the volume, temperature, pressure, and mass of the mixture, we can calculate the number of moles of hydrogen and oxygen. The ratio of the number of moles of hydrogen to the number of moles of oxygen will be 2:1.

Step-by-step explanation:

To find the ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture, we first need to calculate the number of moles of each gas. We can use the ideal gas law, which states that 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.

Given: volume = 2000 cm³, temperature = 300 K, pressure = 100 kPa, mass = 0.76 g

First, we need to convert the volume from cm³ to L (1 L = 1000 cm³):

volume = 2000 cm³ ÷ 1000 = 2 L

Next, we can calculate the number of moles using the ideal gas law:

n = PV / RT = (100 kPa) * (2 L) / (8.3 J/K/mol * 300 K) = 0.824 mol

Since the balanced chemical equation for the reaction between hydrogen and oxygen is 2H₂(g) + O₂(g) -> 2H₂O(g), the ratio of the number of moles of hydrogen to the number of moles of oxygen is 2:1. Therefore, in the mixture, the ratio of the number of moles of hydrogen to the number of moles of oxygen will also be 2:1.

Answer 2

The ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture can be determined using the ideal gas law. The ratio is approximately 2:1.

Step-by-step explanation:

The ratio of the number of moles of hydrogen to the number of moles of oxygen in a mixture can be determined using the ideal gas law. The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. In this case, we are given the volume, temperature, pressure, and mass of the mixture. First, we need to calculate the number of moles of the mixture using the mass and molar mass of the mixture. Molar mass of H2O = 2(1) + 16 = 18 g/mol.

Number of moles = mass / molar mass = 0.76 g / 18 g/mol = 0.0422 mol

Next, we can use the ideal gas law to calculate the number of moles of hydrogen and oxygen in the mixture. Since the ratio of the number of moles of hydrogen to the number of moles of oxygen in water is 2:1, we can determine the ratio in the mixture as well.

Using the ideal gas law: PV = nRT

For hydrogen: (100 kPa) * (2000 cm³) = nH₂ * (8.3 J K⁻¹ mol⁻¹) * (300 K)

For oxygen: (100 kPa) * (2000 cm³) = nO₂ * (8.3 J K⁻¹ mol⁻¹) * (300 K)

Simplifying the equations, we have:

nH₂ = 0.063 mol

nO₂ = 0.0315 mol

Therefore, the ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture is approximately 2:1.