A 2.35 g sample of a substance suspected of being pure gold is warmed to 72.2 ∘C and submerged into 15.5 g of water initially at 24.1 ∘C. The final temperature of the mixture is 26.5 ∘C.
Part A
What is the heat capacity of the unknown substance?
Part B
Could the substance be pure gold?
yes or no?
To find the heat capacity of the unknown substance (Part A), we can use the equation:
Q = m * c * ΔT
where Q is the amount of heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat transferred to the water.
Q_water = m_water * c_water * ΔT_water
Given:
m_water = 15.5 g
c_water = 4.18 J/g⋅°C (specific heat capacity of water)
ΔT_water = final temperature - initial temperature = (26.5 - 24.1) °C = 2.4 °C
Q_water = (15.5 g) * (4.18 J/g⋅°C) * (2.4 °C)
Q_water ≈ 186.528 J
Next, let's find the heat transferred to the unknown substance.
Q_substance = m_substance * c_substance * ΔT_substance
Given:
m_substance = 2.35 g
ΔT_substance = (final temperature - initial temperature = (26.5 - 72.2) °C = -45.7 °C (negative because the substance is losing heat)
Q_substance = (2.35 g) * (c_substance) * (-45.7 °C) = -106.9595 * c_substance [Since the heat is transferred out of the system, the value is negative.]
Finally, the total heat transferred is zero:
Q_total = Q_water + Q_substance
0 = 186.528 J - 106.9595 * c_substance
Now, we can solve for the unknown specific heat capacity (c_substance).
106.9595 * c_substance = 186.528 J
c_substance = 186.528 J / 106.9595
c_substance ≈ 1.74 J/g⋅°C
Therefore, the heat capacity of the unknown substance is approximately 1.74 J/g⋅°C.
To determine whether the substance is pure gold (Part B), we compare its specific heat capacity of approximately 1.74 J/g⋅°C to that of pure gold, which is about 0.129 J/g⋅°C.
Since the specific heat capacity of the unknown substance does not closely match the value for pure gold, the substance is unlikely to be pure gold.
Therefore, the answer to Part B is no, the substance is not likely to be pure gold.
Part A: To find the heat capacity of the unknown substance, we can use the equation:
q = m * c * ΔT
where q is the heat transferred, m is the mass of the substance, c is the heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat transferred to the water. The specific heat capacity of water is generally considered to be 4.184 J/(g⋅°C). Using the equation above, we have:
q_water = m_water * c_water * ΔT_water
where m_water is the mass of water and ΔT_water is the change in temperature of water.
Given:
m_water = 15.5 g (mass of water)
c_water = 4.184 J/(g⋅°C) (specific heat of water)
ΔT_water = (final temperature of the mixture - initial temperature of water) = 26.5 °C - 24.1 °C
Now, let's calculate q_water:
q_water = 15.5 g * 4.184 J/(g⋅°C) * (26.5 °C - 24.1 °C)
Next, let's calculate the heat transferred to the unknown substance:
q_substance = m_substance * c_substance * ΔT_substance
where m_substance is the mass of the unknown substance and ΔT_substance is the change in temperature of the unknown substance.
Given:
m_substance = 2.35 g (mass of the unknown substance)
ΔT_substance = (final temperature of the mixture - initial temperature of the unknown substance) = 26.5 °C - 72.2 °C
Now, let's calculate q_substance by rearranging the equation:
q_substance = q - q_water
Finally, the heat capacity (c_substance) of the unknown substance can be calculated using the equation:
c_substance = q_substance / (m_substance * ΔT_substance)
Part B: The heat capacity of gold is known to be around 0.129 J/(g⋅°C). Compare the heat capacity of the unknown substance (c_substance) calculated in Part A with the known heat capacity of gold. If the heat capacity of the unknown substance is close to the known heat capacity of gold, then it is likely that the substance is pure gold.
it is not pure gold
for connexus answers are
1. B
2. D
3. C
4. D