When a 16.9-g sample of NaOH dissolves in 70.0 g of water in a calorimeter, the temperature rises from 22.4°C to 86.6°C.
And your question is?
To calculate the heat evolved when a sample of NaOH dissolves in water, you can use the equation:
q = m * C * ΔT
where:
q = heat evolved or absorbed (in joules)
m = mass of the solution (in grams)
C = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (final temperature - initial temperature)
Given:
Mass of NaOH = 16.9 g
Mass of water = 70.0 g
Initial temperature = 22.4°C
Final temperature = 86.6°C
Step 1: Calculate the mass of the solution (NaOH + water)
Total mass = mass of NaOH + mass of water
Total mass = 16.9 g + 70.0 g
Total mass = 86.9 g
Step 2: Calculate the change in temperature
ΔT = final temperature - initial temperature
ΔT = 86.6°C - 22.4°C
ΔT = 64.2°C
Step 3: Plug the values into the heat equation
q = m * C * ΔT
q = 86.9 g * 4.18 J/g°C * 64.2°C
Now, multiply the values together:
q ≈ 22921.366 J
The heat evolved when the 16.9 g sample of NaOH dissolves in 70.0 g of water is approximately 22921.366 Joules.
To find the heat released or absorbed during the dissolution process, we can use the formula:
q = m × c × ΔT
Where:
q is the heat energy (in joules),
m is the mass of the solution or substance (in grams),
c is the specific heat capacity of the solution or substance (in J/g°C),
ΔT is the change in temperature (in °C).
First, let's calculate the heat released or absorbed by water during the process.
The mass of water (m₁) is given as 70.0 g.
The specific heat capacity of water (c₁) is 4.18 J/g°C.
The change in temperature (ΔT₁) is (86.6°C - 22.4°C) = 64.2°C.
Using the formula, we can determine the heat absorbed by the water (q₁):
q₁ = m₁ × c₁ × ΔT₁
= 70.0 g × 4.18 J/g°C × 64.2°C
= 18,134.76 J
Next, let's calculate the heat released or absorbed by the NaOH during the process.
The mass of NaOH (m₂) is given as 16.9 g.
The specific heat capacity of NaOH (c₂) is not provided, but we can assume it to be around 4.18 J/g°C (similar to water).
The change in temperature (ΔT₂) is the same as ΔT₁, which is 64.2°C.
Using the formula, we can determine the heat absorbed by the NaOH (q₂):
q₂ = m₂ × c₂ × ΔT₂
= 16.9 g × 4.18 J/g°C × 64.2°C
= 4,840.548 J
To find the total heat released or absorbed (q) during the dissolution process, we need to consider the signs. Since the temperature rose, heat was absorbed, so q is positive:
q = q₁ + q₂
= 18,134.76 J + 4,840.548 J
≈ 22,975.308 J
Therefore, the total heat released or absorbed during the dissolution of NaOH in water is approximately 22,975.308 J.