Answer:
The IV will run ![66.67 \ ml /hr](https://tex.z-dn.net/?f=66.67%20%5C%20ml%20%2Fhr)
Step-by-step explanation:
From the question we are told that
The mass of Magnesium sulfate is ![m_g = 30 \ g](https://tex.z-dn.net/?f=m_g%20%20%3D%20%2030%20%5C%20g)
The volume of the Magnesium sulfate ![V_R = 500ml](https://tex.z-dn.net/?f=V_R%20%20%3D%20500ml)
The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is ![R = 4g/hr](https://tex.z-dn.net/?f=R%20%20%3D%204g%2Fhr)
The concentration of Magnesium sulfate in Lactated Ringers is mathematically evaluated as
![C_m = \frac{m_g}{V_R}](https://tex.z-dn.net/?f=C_m%20%20%3D%20%20%5Cfrac%7Bm_g%7D%7BV_R%7D)
substituting values
![C_m = \frac{30}{500}](https://tex.z-dn.net/?f=C_m%20%20%3D%20%20%5Cfrac%7B30%7D%7B500%7D)
![C_m = 0.06\ g/ ml](https://tex.z-dn.net/?f=C_m%20%20%3D%200.06%5C%20g%2F%20ml)
This implies that
0.06 g of Magnesium sulfate is in every 1 ml of Lactated Ringers
So 4 g of Magnesium sulfate is in x ml of Lactated Ringers
So
![x = \frac{4}{0.06}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B4%7D%7B0.06%7D)
![x = 66.67 \ ml](https://tex.z-dn.net/?f=x%20%3D%20%2066.67%20%5C%20ml)
So the amount of the solution in ml that is been infused in 1 hour is
![66.67 \ ml /hr](https://tex.z-dn.net/?f=66.67%20%5C%20ml%20%2Fhr)