a 23.8 g sample of unknown metal heated at 100 degrees c is placed in 50.0 mL of water at 24 degrees c resulting in 8.5 c temperature increase. What is the specific heat of the metal
1.11J
To find the specific heat of the metal, we can use the formula:
\[ q = mcΔT \]
Where:
- \( q \) is the heat absorbed or released
- \( m \) is the mass of the substance (metal)
- \( c \) is the specific heat capacity of the substance (metal)
- \( ΔT \) is the change in temperature
In this case, we know:
- Mass of the metal, \( m = 23.8 \, \text{g} \)
- Change in temperature, \( ΔT = 8.5 \, ^\circ \text{C} \)
We need to determine the specific heat capacity of the metal, \( c \).
First, let's find the heat absorbed by the water. We can use the formula:
\[ q_{\text{water}} = mcΔT \]
Where:
- \( q_{\text{water}} \) is the heat absorbed or released by the water
- \( m \) is the mass of the water
- \( c \) is the specific heat capacity of water
- \( ΔT \) is the change in temperature
Given:
- Mass of the water, \( m_{\text{water}} = 50.0 \, \text{mL} \)
- Density of water, \( \rho_{\text{water}} = 1 \, \text{g/mL} \)
- Specific heat capacity of water, \( c_{\text{water}} = 4.18 \, \text{J/g°C} \)
First, we convert the mass of the water to grams:
\[ m_{\text{water}} = 50.0 \, \text{mL} \times 1 \, \text{g/mL} = 50.0 \, \text{g} \]
Now, we can calculate the heat absorbed by the water:
\[ q_{\text{water}} = m_{\text{water}} \times c_{\text{water}} \times ΔT \]
\[ q_{\text{water}} = 50.0 \, \text{g} \times 4.18 \, \text{J/g°C} \times 8.5 \, ^\circ \text{C} \]
Next, we calculate the heat absorbed by the metal using the same formula:
\[ q_{\text{metal}} = m_{\text{metal}} \times c_{\text{metal}} \times ΔT \]
Now, we can rearrange the formula to isolate the specific heat capacity of the metal:
\[ c_{\text{metal}} = \frac{{q_{\text{metal}}}}{{m_{\text{metal}} \times ΔT}} \]
Replacing the values we have:
\[ c_{\text{metal}} = \frac{{q_{\text{water}}}}{{m_{\text{metal}} \times ΔT}} \]
\[ c_{\text{metal}} = \frac{{50.0 \, \text{g} \times 4.18 \, \text{J/g°C} \times 8.5 \, ^\circ \text{C}}}{{23.8 \, \text{g} \times 8.5 \, ^\circ \text{C}}} \]
If you calculate that, you'll find the specific heat capacity of the metal.