For the hydrochloric acid at 60 °C the student had collected 30 cm3 after 15 seconds. Calculate the average rate of reaction from 0 to 15 seconds.

The rate of the reaction is approximately 7.315974 × 10⁻⁵ mol/s

Explanation:

The volume occupied by one mole of gas at 60 °C is given from the universal gas equation as follows;

Where;

V = Th volume occupied by the gas

n = The number of moles = 1

R = The universal gas constant = 82.05745 cm³·atm·K⁻¹·mol⁻¹

T = The temperature of the gas = 60°C = 333.15 K

P = The pressure of the gas = 1 atm

By plugging in the values, we get;

The volume of 1 mole of as at 60 °C, V ≈ 27,337.44 cm³/mole

Therefore, the number of moles, 'n', of moles of CO₂ in 30 cm³ of CO₂ is given as follows;

n ≈ 30 cm³/(27,337.44 cm³/mole) ≈ 0.0010973961 moles

Therefore;

The rate of the reaction = Δ[CO₂]/Δt ≈ 0.0010973961 moles/15 s ≈ 7.315974 × 10⁻⁵ mol/s

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.