Respuesta :
Answer:
Explanation:
To find the pressure of the acetylene gas in the cylinder, we can use the ideal gas law equation:
\[PV = nRT\]
Where:
- \(P\) is the pressure of the gas (in atmospheres, atm),
- \(V\) is the volume of the gas (in liters, L),
- \(n\) is the number of moles of gas,
- \(R\) is the ideal gas constant (0.0821 L·atm/mol·K), and
- \(T\) is the temperature of the gas (in Kelvin, K).
First, we need to convert the temperature from Celsius to Kelvin:
\[T(K) = T(°C) + 273.15\]
\[T = 37°C + 273.15 = 310.15 K\]
Now, we can plug the values into the ideal gas law:
\[P \times 55.0 \text{ L} = 10.5 \text{ mol} \times (0.0821 \text{ L} \cdot \text{atm/mol} \cdot \text{K}) \times 310.15 \text{ K}\]
Solving for \(P\):
\[P = \frac{10.5 \times 0.0821 \times 310.15}{55.0}\]
\[P \approx 15.84 \text{ atm}\]
So, the pressure of the acetylene gas in the cylinder is approximately 15.84 atmospheres.
