To solve this problem, we need to use the ideal gas law equation, which is PV = nRT.

First, we need to convert the given values to the appropriate units:

- The pressure (P) is given as 2.00 MPa, which is equal to 2.00 x 10^6 Pa.
- The volume (V) of the cylinder can be calculated using the formula for the volume of a cylinder, V = πr²h. The radius (r) is half of the width, so r = 32.0 cm / 2 = 16.0 cm = 0.16 m. The height (h) is 38.4 cm = 0.384 m. So, V = π(0.16 m)²(0.384 m) = 0.0123 m³.
- The amount of gas (n) can be calculated from the mass of the carbon dioxide and its molar mass. The molar mass of CO2 is approximately 44.01 g/mol. So, n = 0.387 kg / 44.01 g/mol = 8.79 mol.
- The gas constant (R) is 8.314 J/(mol·K).

We can now substitute these values into the ideal gas law equation and solve for the temperature (T):

2.00 x 10^6 Pa * 0.0123 m³ = 8.79 mol * 8.314 J/(mol·K) * T

Solving for T gives:

T = (2.00 x 10^6 Pa * 0.0123 m³) / (8.79 mol * 8.314 J/(mol·K)) = 339.6 K

To convert this temperature to degrees Celsius, we subtract 273.15:

T = 339.6 K - 273.15 = 66.45°C

So, the maximum safe operating temperature the engineer should recommend for this reaction is approximately 66.5°C, rounded to three significant digits.

Question

To solve this problem, we need to use the ideal gas law equation, which is PV = nRT.

First, we need to convert the given values to the appropriate units:

- The pressure (P) is given as 2.00 MPa, which is equal to 2.00 x 10^6 Pa.
- The volume (V) of the cylinder can be calculated using the formula for the volume of a cylinder, V = πr²h. The radius (r) is half of the width, so r = 32.0 cm / 2 = 16.0 cm = 0.16 m. The height (h) is 38.4 cm = 0.384 m. So, V = π(0.16 m)²(0.384 m) = 0.0123 m³.
- The amount of gas (n) can be calculated from the mass of the carbon dioxide and its molar mass. The molar mass of CO2 is approximately 44.01 g/mol. So, n = 0.387 kg / 44.01 g/mol = 8.79 mol.
- The gas constant (R) is 8.314 J/(mol·K).

We can now substitute these values into the ideal gas law equation and solve for the temperature (T):

2.00 x 10^6 Pa * 0.0123 m³ = 8.79 mol * 8.314 J/(mol·K) * T

Solving for T gives:

T = (2.00 x 10^6 Pa * 0.0123 m³) / (8.79 mol * 8.314 J/(mol·K)) = 339.6 K

To convert this temperature to degrees Celsius, we subtract 273.15:

T = 339.6 K - 273.15 = 66.45°C

So, the maximum safe operating temperature the engineer should recommend for this reaction is approximately 66.5°C, rounded to three significant digits.

Knowee AI · Accepted Answer

To solve this problem, we need to use the ideal gas law equation, which is PV = nRT.

First, we need to convert the given values to the appropriate units:

- The pressure (P) is given as 2.00 MPa, which is equal to 2.00 x 10^6 Pa.
- The volume (V) of the cylinder can be calculated using the formula for the volume of a cylinder, V = πr²h. The radius (r) is half of the width, so r = 32.0 cm / 2 = 16.0 cm = 0.16 m. The height (h) is 38.4 cm = 0.384 m. So, V = π(0.16 m)²(0.384 m) = 0.0123 m³.
- The amount of gas (n) can be calculated from the mass of the carbon dioxide and its molar mass. The molar mass of CO2 is approximately 44.01 g/mol. So, n = 0.387 kg / 44.01 g/mol = 8.79 mol.
- The gas constant (R) is 8.314 J/(mol·K).

We can now substitute these values into the ideal gas law equation and solve for the temperature (T):

2.00 x 10^6 Pa * 0.0123 m³ = 8.79 mol * 8.314 J/(mol·K) * T

Solving for T gives:

T = (2.00 x 10^6 Pa * 0.0123 m³) / (8.79 mol * 8.314 J/(mol·K)) = 339.6 K

To convert this temperature to degrees Celsius, we subtract 273.15:

T = 339.6 K - 273.15 = 66.45°C

So, the maximum safe operating temperature the engineer should recommend for this reaction is approximately 66.5°C, rounded to three significant digits.

Question

Solution

Similar Questions

Upgrade your grade with Knowee